--------------------------------------------------------------------------------------------------------------------------------
      name:  OuPowerPaper
       log:  D:\JoPReplication.log
  log type:  text
 opened on:  12 Dec 2022, 14:52:54

. use PowerExperimentsAllinOne,replace

. 
. 
. 
. ************************************************************************************
. * Ou: "Race to the Top: How Competition for Political Power Affects Participation" *
. * Note: All commands are compiled in this one Do file (based on STATA Version 15)  * 
. * The analysis is organized by Experiment.                                         *
. ************************************************************************************
. 
. 
. 
. 
. 
. //As noted in the paper, I focus on voting for one's own group's preferred policy as the main dependent variable//
. //Subjects rarely voted for the policy preferred by the other group and most of such other party voting happened in the first 
> few periods//
. //Whether including voting for the policy preferred by the other group or not does not change our conclusions//
. //Analysis of voting for the policy preferred by the other group is reported later in this replication file//
. 
. gen Voting=0

. replace Voting=1 if GroupA==1&Vote==1
(2,205 real changes made)

. replace Voting=1 if GroupA==0&Vote==2
(3,849 real changes made)

. 
. ********************************************************************************
. *                                                                              *
. *                      Statistical Analysis of Experiment I                    *
. *                                                                              *
. ********************************************************************************          
. 
. preserve

. keep if Experiment==1
(9,700 observations deleted)

. ///Generate Electorate Average of Group A Voters' Voting by Voting Game and Treatment///
> ///Group A's Voting in VG1 of Treatment Group///
> sort UniqueGroupIDbyElectorate

. by UniqueGroupIDbyElectorate: egen AVG1Treatment=mean(Voting) if GroupA==1&VotingGame==1&Treatment==1
(5760 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupAVG1Treatment=mean(AVG1Treatment)
(5120 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupAVG1TreatmentAvg=GroupAVG1Treatment if _n==1
(6,384 missing values generated)

. ///Group A's Voting in VG2 of Treatment Group///
> by UniqueGroupIDbyElectorate: egen AVG2Treatment=mean(Voting) if GroupA==1&VotingGame==2&Treatment==1
(5760 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupAVG2Treatment=mean(AVG2Treatment)
(5120 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupAVG2TreatmentAvg=GroupAVG2Treatment if _n==2
(6,384 missing values generated)

. ///Group A's Voting in VG1 of Control Group///
> sort UniqueGroupIDbyElectorate

. by UniqueGroupIDbyElectorate: egen AVG1Control=mean(Voting) if GroupA==1&VotingGame==1&Treatment==0
(5760 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupAVG1Control=mean(AVG1Control)
(5120 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupAVG1ControlAvg=GroupAVG1Control if _n==1
(6,384 missing values generated)

. ///Group A's Voting in VG2 of Control Group///
> by UniqueGroupIDbyElectorate: egen AVG2Control=mean(Voting) if GroupA==1&VotingGame==2&Treatment==0
(5760 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupAVG2Control=mean(AVG2Control)
(5120 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupAVG2ControlAvg=GroupAVG2Control if _n==2
(6,384 missing values generated)

. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ///Group B's Voting in VG1 of Treatment Group///
> sort UniqueGroupIDbyElectorate

. by UniqueGroupIDbyElectorate: egen BVG1Treatment=mean(Voting) if GroupA==0&VotingGame==1&Treatment==1
(5440 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupBVG1Treatment=mean(BVG1Treatment)
(4480 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupBVG1TreatmentAvg=GroupBVG1Treatment if _n==1
(6,384 missing values generated)

. ///Group B's Voting in VG2 of Treatment Group///
> by UniqueGroupIDbyElectorate: egen BVG2Treatment=mean(Voting) if GroupA==0&VotingGame==2&Treatment==1
(5440 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupBVG2Treatment=mean(BVG2Treatment)
(4480 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupBVG2TreatmentAvg=GroupBVG2Treatment if _n==2
(6,384 missing values generated)

. ///Group B's Voting in VG1 of Control Group///
> sort UniqueGroupIDbyElectorate

. by UniqueGroupIDbyElectorate: egen BVG1Control=mean(Voting) if GroupA==0&VotingGame==1&Treatment==0
(5440 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupBVG1Control=mean(BVG1Control)
(4480 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupBVG1ControlAvg=GroupBVG1Control if _n==1
(6,384 missing values generated)

. ///Group B's Voting in VG2 of Control Group///
> by UniqueGroupIDbyElectorate: egen BVG2Control=mean(Voting) if GroupA==0&VotingGame==2&Treatment==0
(5440 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupBVG2Control=mean(BVG2Control)
(4480 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupBVG2ControlAvg=GroupBVG2Control if _n==2
(6,384 missing values generated)

. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ///Comparisons of Group A's Voting in VG1 Across Treatments/// pp.13 of manuscript
> gen AVG1AcrossTreatments=GroupAVG1TreatmentAvg if Treatment==1
(6,384 missing values generated)

. replace AVG1AcrossTreatments=GroupAVG1ControlAvg if Treatment==0
(16 real changes made)

. 
. ttest AVG1AcrossTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16    .4546875     .043614     .174456    .3617265    .5476485
       1 |      16      .64375    .0392972    .1571888      .55999      .72751
---------+--------------------------------------------------------------------
combined |      32    .5492187    .0334975    .1894904    .4809002    .6175373
---------+--------------------------------------------------------------------
    diff |           -.1890625    .0587065               -.3089571   -.0691678
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -3.2205
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0015         Pr(|T| > |t|) = 0.0031          Pr(T > t) = 0.9985

. ranksum AVG1AcrossTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16         187         264
           1 |       16         341         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -5.03
                     ----------
adjusted variance        698.97

Ho: AVG1Ac~s(Treatm~t==0) = AVG1Ac~s(Treatm~t==1)
             z =  -2.912
    Prob > |z| =   0.0036

. 
. ///Comparisons of Group B's Voting in VG1 Across Treatments/// pp.13 of manuscript
> gen BVG1AcrossTreatments=GroupBVG1TreatmentAvg if Treatment==1
(6,384 missing values generated)

. replace BVG1AcrossTreatments=GroupBVG1ControlAvg if Treatment==0
(16 real changes made)

. 
. ttest BVG1AcrossTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16      .23125    .0423247    .1692987    .1410371    .3214629
       1 |      16    .4364583       .0393    .1571999    .3526924    .5202242
---------+--------------------------------------------------------------------
combined |      32    .3338542    .0338624    .1915549    .2647913    .4029171
---------+--------------------------------------------------------------------
    diff |           -.2052083    .0577569               -.3231638   -.0872529
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -3.5530
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0006         Pr(|T| > |t|) = 0.0013          Pr(T > t) = 0.9994

. ranksum BVG1AcrossTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16         185         264
           1 |       16         343         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -2.06
                     ----------
adjusted variance        701.94

Ho: BVG1Ac~s(Treatm~t==0) = BVG1Ac~s(Treatm~t==1)
             z =  -2.982
    Prob > |z| =   0.0029

. 
. ///Comparisons of Group A's Voting in VG2 Across Treatments/// pp.13 of manuscript
> gen AVG2AcrossTreatments=GroupAVG2TreatmentAvg if Treatment==1
(6,384 missing values generated)

. replace AVG2AcrossTreatments=GroupAVG2ControlAvg if Treatment==0
(16 real changes made)

. 
. ttest AVG2AcrossTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16    .1203125    .0385424    .1541695    .0381614    .2024636
       1 |      16     .340625    .0479732     .191893    .2383724    .4428776
---------+--------------------------------------------------------------------
combined |      32    .2304688    .0361612    .2045584    .1567176    .3042199
---------+--------------------------------------------------------------------
    diff |           -.2203125    .0615382               -.3459902   -.0946348
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -3.5801
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0006         Pr(|T| > |t|) = 0.0012          Pr(T > t) = 0.9994

. ranksum AVG2AcrossTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16         176         264
           1 |       16         352         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -3.61
                     ----------
adjusted variance        700.39

Ho: AVG2Ac~s(Treatm~t==0) = AVG2Ac~s(Treatm~t==1)
             z =  -3.325
    Prob > |z| =   0.0009

. 
. ///Comparisons of Group B's Voting in VG2 Across Treatments/// pp.13 of manuscript
> gen BVG2AcrossTreatments=GroupBVG2TreatmentAvg if Treatment==1
(6,384 missing values generated)

. replace BVG2AcrossTreatments=GroupBVG2ControlAvg if Treatment==0
(16 real changes made)

. 
. ttest BVG2AcrossTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16    .3489583    .0519408    .2077631    .2382492    .4596675
       1 |      16    .5385417    .0447917    .1791667    .4430705    .6340128
---------+--------------------------------------------------------------------
combined |      32      .44375    .0377882    .2137626    .3666804    .5208196
---------+--------------------------------------------------------------------
    diff |           -.1895833    .0685867               -.3296561   -.0495106
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.7641
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0048         Pr(|T| > |t|) = 0.0097          Pr(T > t) = 0.9952

. ranksum BVG2AcrossTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16       192.5         264
           1 |       16       335.5         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -2.32
                     ----------
adjusted variance        701.68

Ho: BVG2Ac~s(Treatm~t==0) = BVG2Ac~s(Treatm~t==1)
             z =  -2.699
    Prob > |z| =   0.0070

. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ///Comparisons of Group A' Voting in Control Across VGs/// pp.13 of manuscript
> gen GroupAControlAcrossVGs=GroupAVG1ControlAvg if  Treatment==0&GroupAVG1ControlAvg!=.
(6,384 missing values generated)

. replace GroupAControlAcrossVGs=GroupAVG2ControlAvg if Treatment==0&GroupAVG2ControlAvg!=.
(16 real changes made)

. 
. gen withinControlA=0 if GroupAVG1ControlAvg!=.
(6,384 missing values generated)

. replace withinControlA=1 if GroupAVG2ControlAvg!=.
(16 real changes made)

. 
. ttest GroupAControlAcrossVGs,by(withinControlA)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16    .4546875     .043614     .174456    .3617265    .5476485
       1 |      16    .1203125    .0385424    .1541695    .0381614    .2024636
---------+--------------------------------------------------------------------
combined |      32       .2875    .0414882    .2346927    .2028843    .3721157
---------+--------------------------------------------------------------------
    diff |             .334375    .0582039                .2155068    .4532432
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   5.7449
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 1.0000         Pr(|T| > |t|) = 0.0000          Pr(T > t) = 0.0000

. ranksum GroupAControlAcrossVGs,by(withinControlA)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

withinCont~A |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16       367.5         264
           1 |       16       160.5         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -4.13
                     ----------
adjusted variance        699.87

Ho: GroupA~s(within~A==0) = GroupA~s(within~A==1)
             z =   3.912
    Prob > |z| =   0.0001

. 
. ///Comparisons of Group A's Voting in Treatment Across VGs/// pp.13 of manuscript
> gen GroupATreatmentAcrossVGs=GroupAVG1TreatmentAvg if  Treatment==1&GroupAVG1TreatmentAvg!=.
(6,384 missing values generated)

. replace GroupATreatmentAcrossVGs=GroupAVG2TreatmentAvg if Treatment==1&GroupAVG2TreatmentAvg!=.
(16 real changes made)

. 
. gen withinTreatmentA=0 if GroupAVG1TreatmentAvg!=.
(6,384 missing values generated)

. replace withinTreatmentA=1 if GroupAVG2TreatmentAvg!=.
(16 real changes made)

. 
. ttest GroupATreatmentAcrossVGs,by(withinTreatmentA)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16      .64375    .0392972    .1571888      .55999      .72751
       1 |      16     .340625    .0479732     .191893    .2383724    .4428776
---------+--------------------------------------------------------------------
combined |      32    .4921875     .040883    .2312691    .4088061    .5755689
---------+--------------------------------------------------------------------
    diff |             .303125    .0620137                .1764761    .4297739
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   4.8880
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 1.0000         Pr(|T| > |t|) = 0.0000          Pr(T > t) = 0.0000

. ranksum GroupATreatmentAcrossVGs,by(withinTreatmentA)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

withinTrea~A |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16         356         264
           1 |       16         172         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -2.06
                     ----------
adjusted variance        701.94

Ho: G~Trea~s(withi~tA==0) = G~Trea~s(withi~tA==1)
             z =   3.472
    Prob > |z| =   0.0005

. 
. ///Comparisons of Group B' Voting in Control Across VGs/// pp.13 of manuscript
> gen GroupBControlAcrossVGs=GroupBVG1ControlAvg if  Treatment==0&GroupBVG1ControlAvg!=.
(6,384 missing values generated)

. replace GroupBControlAcrossVGs=GroupBVG2ControlAvg if Treatment==0&GroupBVG2ControlAvg!=.
(16 real changes made)

. 
. gen withinControlB=0 if GroupBVG1ControlAvg!=.
(6,384 missing values generated)

. replace withinControlB=1 if GroupBVG2ControlAvg!=.
(16 real changes made)

. 
. ttest GroupBControlAcrossVGs,by(withinControlB)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16      .23125    .0423247    .1692987    .1410371    .3214629
       1 |      16    .3489583    .0519408    .2077631    .2382492    .4596675
---------+--------------------------------------------------------------------
combined |      32    .2901042    .0346098    .1957826     .219517    .3606913
---------+--------------------------------------------------------------------
    diff |           -.1177083    .0670017                -.254544    .0191273
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -1.7568
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0446         Pr(|T| > |t|) = 0.0892          Pr(T > t) = 0.9554

. ranksum GroupBControlAcrossVGs,by(withinControlB)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

withinCont~B |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16         221         264
           1 |       16         307         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -4.52
                     ----------
adjusted variance        699.48

Ho: GroupB~s(within~B==0) = GroupB~s(within~B==1)
             z =  -1.626
    Prob > |z| =   0.1040

. 
. ///Comparisons of Group B' Voting in Treatment Across VGs/// pp.13 of manuscript
> gen GroupBTreatmentAcrossVGs=GroupBVG1TreatmentAvg if  Treatment==1&GroupBVG1TreatmentAvg!=.
(6,384 missing values generated)

. replace GroupBTreatmentAcrossVGs=GroupBVG2TreatmentAvg if Treatment==1&GroupBVG2TreatmentAvg!=.
(16 real changes made)

. 
. gen withinTreatmentB=0 if GroupBVG1TreatmentAvg!=.
(6,384 missing values generated)

. replace withinTreatmentB=1 if GroupBVG2TreatmentAvg!=.
(16 real changes made)

. 
. ttest GroupBTreatmentAcrossVGs,by(withinTreatmentB)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16    .4364583       .0393    .1571999    .3526924    .5202242
       1 |      16    .5385417    .0447917    .1791667    .4430705    .6340128
---------+--------------------------------------------------------------------
combined |      32       .4875    .0307099    .1737216    .4248667    .5501333
---------+--------------------------------------------------------------------
    diff |           -.1020833    .0595884               -.2237791    .0196125
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -1.7131
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0485         Pr(|T| > |t|) = 0.0970          Pr(T > t) = 0.9515

. ranksum GroupBTreatmentAcrossVGs,by(withinTreatmentB)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

withinTrea~B |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16       212.5         264
           1 |       16       315.5         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -1.68
                     ----------
adjusted variance        702.32

Ho: GroupBT~(withi~tB==0) = GroupBT~(withi~tB==1)
             z =  -1.943
    Prob > |z| =   0.0520

. 
. 
. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ///To complement the nonparametric statistical tests reported above, I also conduct 
> ///a regression-based statistical analysis that uses all observations 
> ///and cluster-robust standard errors that allow for arbitrary correlation between 
> ///observations from the same electorate. These results are reported in Appendix E
> ///////////////         Table A1 (Appendix E)        ///////////////////////////
> 
. logit Voting Treatment if GroupA==1&VotingGame==1,vce(cluster UniqueElectorateID)

Iteration 0:   log pseudolikelihood = -881.01677  
Iteration 1:   log pseudolikelihood = -857.78138  
Iteration 2:   log pseudolikelihood = -857.76967  
Iteration 3:   log pseudolikelihood = -857.76967  

Logistic regression                             Number of obs     =      1,280
                                                Wald chi2(1)      =      10.25
                                                Prob > chi2       =     0.0014
Log pseudolikelihood = -857.76967               Pseudo R2         =     0.0264

                    (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
------------------------------------------------------------------------------
             |               Robust
      Voting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   Treatment |   .7734264   .2415727     3.20   0.001     .2999526      1.2469
       _cons |  -.1817487   .1730403    -1.05   0.294    -.5209014    .1574041
------------------------------------------------------------------------------

. eststo margin11: margins, dydx(*) atmeans  post

Conditional marginal effects                    Number of obs     =      1,280
Model VCE    : Robust

Expression   : Pr(Voting), predict()
dy/dx w.r.t. : Treatment
at           : Treatment       =          .5 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   Treatment |     .19134   .0598716     3.20   0.001     .0739937    .3086862
------------------------------------------------------------------------------

. estimates store m11, title(Model 1)

. logit Voting Treatment if GroupA==0&VotingGame==1,vce(cluster UniqueElectorateID)

Iteration 0:   log pseudolikelihood = -1222.7992  
Iteration 1:   log pseudolikelihood = -1177.0873  
Iteration 2:   log pseudolikelihood = -1176.7993  
Iteration 3:   log pseudolikelihood = -1176.7992  

Logistic regression                             Number of obs     =      1,920
                                                Wald chi2(1)      =      11.24
                                                Prob > chi2       =     0.0008
Log pseudolikelihood = -1176.7992               Pseudo R2         =     0.0376

                    (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
------------------------------------------------------------------------------
             |               Robust
      Voting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   Treatment |    .945718   .2820652     3.35   0.001     .3928803    1.498556
       _cons |  -1.201266   .2342105    -5.13   0.000    -1.660311   -.7422221
------------------------------------------------------------------------------

. eststo margin12: margins,  dydx(*) atmeans  post

Conditional marginal effects                    Number of obs     =      1,920
Model VCE    : Robust

Expression   : Pr(Voting), predict()
dy/dx w.r.t. : Treatment
at           : Treatment       =          .5 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   Treatment |   .2076468   .0588248     3.53   0.000     .0923523    .3229412
------------------------------------------------------------------------------

. estimates store m12, title(Model 2)

. logit Voting Treatment if GroupA==1&VotingGame==2,vce(cluster UniqueElectorateID)

Iteration 0:   log pseudolikelihood = -690.99791  
Iteration 1:   log pseudolikelihood = -647.10969  
Iteration 2:   log pseudolikelihood = -645.76067  
Iteration 3:   log pseudolikelihood = -645.75765  
Iteration 4:   log pseudolikelihood = -645.75765  

Logistic regression                             Number of obs     =      1,280
                                                Wald chi2(1)      =      10.24
                                                Prob > chi2       =     0.0014
Log pseudolikelihood = -645.75765               Pseudo R2         =     0.0655

                    (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
------------------------------------------------------------------------------
             |               Robust
      Voting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   Treatment |   1.328964   .4153188     3.20   0.001      .514954    2.142974
       _cons |  -1.989474   .3582441    -5.55   0.000     -2.69162   -1.287329
------------------------------------------------------------------------------

. eststo margin13: margins,  dydx(*) atmeans  post

Conditional marginal effects                    Number of obs     =      1,280
Model VCE    : Robust

Expression   : Pr(Voting), predict()
dy/dx w.r.t. : Treatment
at           : Treatment       =          .5 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   Treatment |   .2204666   .0605495     3.64   0.000     .1017918    .3391414
------------------------------------------------------------------------------

. estimates store m13, title(Model 3)

. logit Voting Treatment if GroupA==0&VotingGame==2,vce(cluster UniqueElectorateID)

Iteration 0:   log pseudolikelihood = -1318.6668  
Iteration 1:   log pseudolikelihood = -1283.5157  
Iteration 2:   log pseudolikelihood = -1283.4938  
Iteration 3:   log pseudolikelihood = -1283.4938  

Logistic regression                             Number of obs     =      1,920
                                                Wald chi2(1)      =       7.38
                                                Prob > chi2       =     0.0066
Log pseudolikelihood = -1283.4938               Pseudo R2         =     0.0267

                    (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
------------------------------------------------------------------------------
             |               Robust
      Voting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   Treatment |   .7780942    .286394     2.72   0.007     .2167724    1.339416
       _cons |  -.6236211   .2249085    -2.77   0.006    -1.064434   -.1828086
------------------------------------------------------------------------------

. eststo margin14: margins, dydx(*) atmeans  post

Conditional marginal effects                    Number of obs     =      1,920
Model VCE    : Robust

Expression   : Pr(Voting), predict()
dy/dx w.r.t. : Treatment
at           : Treatment       =          .5 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   Treatment |    .191872   .0699433     2.74   0.006     .0547856    .3289584
------------------------------------------------------------------------------

. estimates store m14, title(Model 4)

. esttab margin11 margin12 margin13 margin14 using TableA1.txt,cells(b(star fmt(3))/* 
> */se(par fmt(3))) star(* 0.10 ** 0.05 *** 0.01) stats(r2_a N,fmt(%9.3f %9.0g)) legend label collabels(none) replace
(note: file TableA1.txt not found)
(output written to TableA1.txt)

. restore

. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> preserve

. keep if Experiment==1
(9,700 observations deleted)

. keep if Period==40  
(6,240 observations deleted)

. //Examine Elicited Valuation of Participation by Voter and Treatment (Figure 3)//
. *post-treatment survey was conducted right after the 40th round of voting and was elicited once*
. *generate Electorate Average of Valuations by Group and Treatment*
. sort UniqueElectorateID

. by UniqueElectorateID: egen GroupAValue=mean(VotingImportance) if GroupA==1
(96 missing values generated)

. by UniqueElectorateID, sort: egen AMeanValue=mean(GroupAValue)

. by UniqueElectorateID: gen GroupAMeanValue=AMeanValue if _n==1
(128 missing values generated)

. sort UniqueElectorateID

. by UniqueElectorateID: egen GroupBValue=mean(VotingImportance) if GroupA==0
(64 missing values generated)

. by UniqueElectorateID, sort: egen BMeanValue=mean(GroupBValue)

. by UniqueElectorateID: gen GroupBMeanValue=BMeanValue if _n==1
(128 missing values generated)

. 
. ttest GroupAMeanValue,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16     4.71875    .2413881    .9655525    4.204243    5.233257
       1 |      16     5.96875    .2477766    .9911063    5.440627    6.496873
---------+--------------------------------------------------------------------
combined |      32     5.34375     .203841    1.153099    4.928014    5.759486
---------+--------------------------------------------------------------------
    diff |               -1.25    .3459212               -1.956465   -.5435347
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -3.6135
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0005         Pr(|T| > |t|) = 0.0011          Pr(T > t) = 0.9995

. ranksum GroupAMeanValue,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16       183.5         264
           1 |       16       344.5         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties      -15.74
                     ----------
adjusted variance        688.26

Ho: GroupAM~(Treatm~t==0) = GroupAM~(Treatm~t==1)
             z =  -3.068
    Prob > |z| =   0.0022

. 
. ttest GroupBMeanValue,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16        4.75    .3657818    1.463127    3.970355    5.529645
       1 |      16    6.166667    .2704591    1.081837    5.590197    6.743137
---------+--------------------------------------------------------------------
combined |      32    5.458333    .2573951    1.456047    4.933373    5.983294
---------+--------------------------------------------------------------------
    diff |           -1.416667    .4549115                -2.34572   -.4876135
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -3.1142
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0020         Pr(|T| > |t|) = 0.0040          Pr(T > t) = 0.9980

. ranksum GroupBMeanValue,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16       191.5         264
           1 |       16       336.5         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -4.90
                     ----------
adjusted variance        699.10

Ho: GroupBM~(Treatm~t==0) = GroupBM~(Treatm~t==1)
             z =  -2.742
    Prob > |z| =   0.0061

. 
. 
. //Examine Elicited Status-Seeking Preferences by Voter and Treatment (Figure 4)//
. *generate Electorate Average of Valuations by Group and Treatment*
. sort UniqueElectorateID

. by UniqueElectorateID: egen GroupAStatus=mean(EarningMorethanOthers) if GroupA==1
(96 missing values generated)

. by UniqueElectorateID, sort: egen AMeanStatus=mean(GroupAStatus)

. by UniqueElectorateID: gen GroupAMeanStatus=AMeanStatus if _n==1
(128 missing values generated)

. sort UniqueElectorateID

. by UniqueElectorateID: egen GroupBStatus=mean(EarningMorethanOthers) if GroupA==0
(64 missing values generated)

. by UniqueElectorateID, sort: egen BMeanStatus=mean(GroupBStatus)

. by UniqueElectorateID: gen GroupBMeanStatus=BMeanStatus if _n==1
(128 missing values generated)

. 
. ttest GroupAMeanStatus,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16      5.6875    .2918154    1.167262     5.06551     6.30949
       1 |      16     7.03125    .2974501      1.1898     6.39725     7.66525
---------+--------------------------------------------------------------------
combined |      32    6.359375     .237844    1.345449    5.874289    6.844461
---------+--------------------------------------------------------------------
    diff |            -1.34375    .4166927                -2.19475     -.49275
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -3.2248
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0015         Pr(|T| > |t|) = 0.0030          Pr(T > t) = 0.9985

. ranksum GroupAMeanStatus,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16         192         264
           1 |       16         336         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -9.16
                     ----------
adjusted variance        694.84

Ho: GroupA..(Treatm~t==0) = GroupA..(Treatm~t==1)
             z =  -2.731
    Prob > |z| =   0.0063

. 
. ttest GroupBMeanStatus,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16    5.104167    .3343301     1.33732    4.391559    5.816774
       1 |      16    6.395833     .262147    1.048588     5.83708    6.954586
---------+--------------------------------------------------------------------
combined |      32        5.75    .2390056     1.35202    5.262545    6.237455
---------+--------------------------------------------------------------------
    diff |           -1.291667    .4248502               -2.159326   -.4240068
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -3.0403
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0024         Pr(|T| > |t|) = 0.0049          Pr(T > t) = 0.9976

. ranksum GroupBMeanStatus,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16       197.5         264
           1 |       16       330.5         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -5.42
                     ----------
adjusted variance        698.58

Ho: GroupB..(Treatm~t==0) = GroupB..(Treatm~t==1)
             z =  -2.516
    Prob > |z| =   0.0119

. restore

. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> 
. ////////////////////////////////////////////////////////////////////////////////
> ///Examine The Likelihood that Policy B Winning Across Treatments (Figure 5)////
> *****recall that each Group A voter has 2 ballots in Exp. I*****
. preserve

. keep if Experiment==1
(9,700 observations deleted)

. 
. gen VoteA=0

. replace VoteA=2 if Vote==1&GroupA==1
(998 real changes made)

. replace VoteA=1 if Vote==1&GroupA==0
(56 real changes made)

. gen VoteB=0

. replace VoteB=2 if Vote==2&GroupA==1
(69 real changes made)

. replace VoteB=1 if Vote==2&GroupA==0
(1,493 real changes made)

. 
. *****compute how many votes are for A and B*****
. by UniqueElectionPeriodID, sort: egen V4A=total(VoteA)

. by UniqueElectionPeriodID, sort: egen V4B=total(VoteB)

. 
. 
. sort UniqueElectorateID Period Subject

. 
. gen ProbBWin=0

. replace ProbBWin=0.5 if V4A==0&V4B==0
(785 real changes made)

. replace ProbBWin=V4B/(V4A+V4B) if V4A+V4B>0
(4,455 real changes made)

. 
. ***generate electorate average of computed likelihood Policy B Wins in VG1******
. sort UniqueElectorateID

. by UniqueElectorateID: egen ProbBWinVG1=mean(ProbBWin) if VotingGame==1
(3200 missing values generated)

. by UniqueElectorateID, sort: egen ProbBWinVG1Avg=mean(ProbBWinVG1)

. by UniqueElectorateID: gen VG1ProbBWinElectorateLevel=ProbBWinVG1Avg if _n==1
(6,368 missing values generated)

. 
. ***generate electorate average of computed likelihood Policy B Wins in VG2******
. sort UniqueElectorateID

. by UniqueElectorateID: egen ProbBWinVG2=mean(ProbBWin) if VotingGame==2
(3200 missing values generated)

. by UniqueElectorateID, sort: egen ProbBWinVG2Avg=mean(ProbBWinVG2)

. by UniqueElectorateID: gen VG2ProbBWinElectorateLevel=ProbBWinVG2Avg if _n==1
(6,368 missing values generated)

. 
. *compare electorate average of computed likelihood Policy B Wins by Voting Game*
. ttest VG1ProbBWinElectorateLevel,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16    .2829613    .0415631    .1662525    .1943716     .371551
       1 |      16    .3754316    .0302853    .1211412      .31088    .4399832
---------+--------------------------------------------------------------------
combined |      32    .3291964    .0266233    .1506044    .2748978    .3834951
---------+--------------------------------------------------------------------
    diff |           -.0924702    .0514266               -.1974973    .0125568
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -1.7981
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0411         Pr(|T| > |t|) = 0.0822          Pr(T > t) = 0.9589

. ranksum VG1ProbBWinElectorateLevel,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16         212         264
           1 |       16         316         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties        0.00
                     ----------
adjusted variance        704.00

Ho: VG1Pro~l(Treatm~t==0) = VG1Pro~l(Treatm~t==1)
             z =  -1.960
    Prob > |z| =   0.0500

. 
. ttest VG2ProbBWinElectorateLevel,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16    .7300595    .0645022    .2580088    .5925763    .8675427
       1 |      16    .5963542    .0414724    .1658897    .5079578    .6847506
---------+--------------------------------------------------------------------
combined |      32    .6632068    .0395837    .2239194    .5824753    .7439384
---------+--------------------------------------------------------------------
    diff |            .1337054    .0766844               -.0229051    .2903158
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   1.7436
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9543         Pr(|T| > |t|) = 0.0915          Pr(T > t) = 0.0457

. ranksum VG2ProbBWinElectorateLevel,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16         319         264
           1 |       16         209         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties        0.00
                     ----------
adjusted variance        704.00

Ho: VG2Pro~l(Treatm~t==0) = VG2Pro~l(Treatm~t==1)
             z =   2.073
    Prob > |z| =   0.0382

. 
. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ///To complement the nonparametric statistical tests reported above, I also conduct 
> ///a regression-based statistical analysis that uses all observations 
> ///and cluster-robust standard errors that allow for arbitrary correlation between 
> ///observations from the same electorate. These results are reported in Appendix E
> ///////////////         Table A2 (Appendix E)        ///////////////////////////
> 
. reg VotingImportance Treatment if GroupA==1,vce(cluster UniqueElectorateID)

Linear regression                               Number of obs     =      2,560
                                                F(1, 31)          =      13.49
                                                Prob > F          =     0.0009
                                                R-squared         =     0.1235
                                                Root MSE          =     1.6657

                    (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
------------------------------------------------------------------------------
             |               Robust
VotingImpo~e |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   Treatment |       1.25   .3403626     3.67   0.001      .555826    1.944174
       _cons |    4.71875   .2375093    19.87   0.000     4.234347    5.203153
------------------------------------------------------------------------------

. outreg2 using TableA2.txt, dec(3) ctitle(Model 1) drop(_Icode*) replace
dir : seeout

. reg EarningMorethanOthers Treatment if GroupA==1,vce(cluster UniqueElectorateID)

Linear regression                               Number of obs     =      2,560
                                                F(1, 31)          =      10.74
                                                Prob > F          =     0.0026
                                                R-squared         =     0.1274
                                                Root MSE          =     1.7589

                    (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
------------------------------------------------------------------------------
             |               Robust
EarningMor~s |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   Treatment |    1.34375   .4099969     3.28   0.003     .5075558    2.179944
       _cons |     5.6875   .2871263    19.81   0.000     5.101902    6.273098
------------------------------------------------------------------------------

. outreg2 using TableA2.txt, dec(3) ctitle(Model 2) drop(_Icode*) append
dir : seeout

. reg VotingImportance Treatment if GroupA==0,vce(cluster UniqueElectorateID)

Linear regression                               Number of obs     =      3,840
                                                F(1, 31)          =      10.02
                                                Prob > F          =     0.0035
                                                R-squared         =     0.1100
                                                Root MSE          =     2.0152

                    (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
------------------------------------------------------------------------------
             |               Robust
VotingImpo~e |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   Treatment |   1.416667   .4475723     3.17   0.003     .5038369    2.329496
       _cons |       4.75   .3598806    13.20   0.000     4.016019    5.483981
------------------------------------------------------------------------------

. outreg2 using TableA2.txt, dec(3) ctitle(Model 3) drop(_Icode*) append
dir : seeout

. reg EarningMorethanOthers Treatment if GroupA==0,vce(cluster UniqueElectorateID)

Linear regression                               Number of obs     =      3,840
                                                F(1, 31)          =       9.55
                                                Prob > F          =     0.0042
                                                R-squared         =     0.0841
                                                Root MSE          =     2.1316

                    (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
------------------------------------------------------------------------------
             |               Robust
EarningMor~s |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   Treatment |   1.291667    .417996     3.09   0.004     .4391581    2.144175
       _cons |   5.104167   .3289363    15.52   0.000     4.433297    5.775037
------------------------------------------------------------------------------

. outreg2 using TableA2.txt, dec(3) ctitle(Model 4) drop(_Icode*) append
dir : seeout

. reg ProbBWin Treatment if VotingGame==1,vce(cluster UniqueElectorateID)

Linear regression                               Number of obs     =      3,200
                                                F(1, 31)          =       3.34
                                                Prob > F          =     0.0773
                                                R-squared         =     0.0273
                                                Root MSE          =      .2763

                    (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
------------------------------------------------------------------------------
             |               Robust
    ProbBWin |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   Treatment |   .0924702   .0505982     1.83   0.077    -.0107255     .195666
       _cons |   .2829613   .0408936     6.92   0.000     .1995582    .3663644
------------------------------------------------------------------------------

. outreg2 using TableA2.txt, dec(3) ctitle(Model 5) drop(_Icode*) append
dir : seeout

. reg ProbBWin Treatment if VotingGame==2,vce(cluster UniqueElectorateID)

Linear regression                               Number of obs     =      3,200
                                                F(1, 31)          =       3.14
                                                Prob > F          =     0.0862
                                                R-squared         =     0.0383
                                                Root MSE          =      .3351

                    (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
------------------------------------------------------------------------------
             |               Robust
    ProbBWin |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   Treatment |  -.1337054   .0754492    -1.77   0.086     -.287585    .0201743
       _cons |   .7300595   .0634632    11.50   0.000     .6006254    .8594937
------------------------------------------------------------------------------

. outreg2 using TableA2.txt, dec(3) ctitle(Model 6) drop(_Icode*) append
dir : seeout

. ////////////////////////////////////////////////////////////////////////////////
> ///////////////         Table A3 (Appendix E)        ///////////////////////////
> 
. reg ProbBWin Period,vce(cluster UniqueElectorateID)

Linear regression                               Number of obs     =      6,400
                                                F(1, 31)          =       0.25
                                                Prob > F          =     0.6236
                                                R-squared         =     0.0019
                                                Root MSE          =     .35391

                    (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
------------------------------------------------------------------------------
             |               Robust
    ProbBWin |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      Period |  -.0013309   .0026846    -0.50   0.624    -.0068061    .0041443
       _cons |   .5234847   .0646295     8.10   0.000      .391672    .6552975
------------------------------------------------------------------------------

. outreg2 using TableA3.txt, dec(3) ctitle(Model 1) drop(_Icode*) replace
dir : seeout

. reg ProbBWin Period if Treatment==0,vce(cluster UniqueElectorateID)

Linear regression                               Number of obs     =      3,200
                                                F(1, 15)          =       0.80
                                                Prob > F          =     0.3864
                                                R-squared         =     0.0146
                                                Root MSE          =     .38464

                    (Std. Err. adjusted for 16 clusters in UniqueElectorateID)
------------------------------------------------------------------------------
             |               Robust
    ProbBWin |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      Period |  -.0040591   .0045497    -0.89   0.386    -.0137565    .0056383
       _cons |   .5897224   .1079221     5.46   0.000     .3596919    .8197529
------------------------------------------------------------------------------

. outreg2 using TableA3.txt, dec(3) ctitle(Model 2) drop(_Icode*) append
dir : seeout

. reg ProbBWin Period if Treatment==1,vce(cluster UniqueElectorateID)

Linear regression                               Number of obs     =      3,200
                                                F(1, 15)          =       0.24
                                                Prob > F          =     0.6306
                                                R-squared         =     0.0026
                                                Root MSE          =     .31693

                    (Std. Err. adjusted for 16 clusters in UniqueElectorateID)
------------------------------------------------------------------------------
             |               Robust
    ProbBWin |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      Period |   .0013974   .0028462     0.49   0.631    -.0046692     .007464
       _cons |    .457247   .0709589     6.44   0.000     .3060017    .6084923
------------------------------------------------------------------------------

. outreg2 using TableA3.txt, dec(3) ctitle(Model 3) drop(_Icode*) append
dir : seeout

. restore

. ////////////////////////////////////////////////////////////////////////////////
> 
. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> *compare task performance across treatments*
. *note that Task Stage was played only once at the beginning of the experiment* 
. preserve

. keep if Experiment==1
(9,700 observations deleted)

. ttest TaskPerformance if Period==1,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      80      10.325    .5658462    5.061083    9.198711    11.45129
       1 |      80     12.4625    .5246891    4.692962    11.41813    13.50687
---------+--------------------------------------------------------------------
combined |     160    11.39375    .3938498     4.98185     10.6159     12.1716
---------+--------------------------------------------------------------------
    diff |             -2.1375    .7716739               -3.661627    -.613373
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.7700
Ho: diff = 0                                     degrees of freedom =      158

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0031         Pr(|T| > |t|) = 0.0063          Pr(T > t) = 0.9969

. ranksum TaskPerformance if Period==1,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       80        5839        6440
           1 |       80        7041        6440
-------------+---------------------------------
    combined |      160       12880       12880

unadjusted variance    85866.67
adjustment for ties     -397.23
                     ----------
adjusted variance      85469.43

Ho: TaskPe~e(Treatm~t==0) = TaskPe~e(Treatm~t==1)
             z =  -2.056
    Prob > |z| =   0.0398

. 
. gen TreatmentTaskPerformance=Treatment*TaskPerformance

. gen VG1=0

. replace VG1=1 if VotingGame==1
(3,200 real changes made)

. gen TreatmentVG1=Treatment*VG1

. 
. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ///////////////////////         Table 2        /////////////////////////////////
> logit Voting Treatment TaskPerformance Period Age Men i.Major CRTScore Competitiveness if GroupA==1,vce(cluster UniqueElectora
> teID)

Iteration 0:   log pseudolikelihood =  -1711.816  
Iteration 1:   log pseudolikelihood = -1580.8195  
Iteration 2:   log pseudolikelihood = -1579.4086  
Iteration 3:   log pseudolikelihood = -1579.4082  
Iteration 4:   log pseudolikelihood = -1579.4082  

Logistic regression                             Number of obs     =      2,560
                                                Wald chi2(11)     =      52.93
                                                Prob > chi2       =     0.0000
Log pseudolikelihood = -1579.4082               Pseudo R2         =     0.0773

                       (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
---------------------------------------------------------------------------------
                |               Robust
         Voting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      Treatment |   .5617043   .2398283     2.34   0.019     .0916494    1.031759
TaskPerformance |   .0662172   .0298722     2.22   0.027     .0076688    .1247657
         Period |  -.0021067   .0124845    -0.17   0.866    -.0265758    .0223624
            Age |  -.0118789   .0498746    -0.24   0.812    -.1096313    .0858735
            Men |    .645437   .2286395     2.82   0.005     .1973118    1.093562
                |
          Major |
             2  |    .045325   .3725714     0.12   0.903    -.6849015    .7755514
             3  |  -.0358487    .285116    -0.13   0.900    -.5946657    .5229684
             5  |  -.2910381   .3584801    -0.81   0.417    -.9936462    .4115699
             6  |  -.3473172   .2547284    -1.36   0.173    -.8465758    .1519413
                |
       CRTScore |  -.2205856   .2825487    -0.78   0.435    -.7743708    .3331996
Competitiveness |  -.0453932   .0458818    -0.99   0.322      -.13532    .0445335
          _cons |  -1.067689   1.132403    -0.94   0.346    -3.287158    1.151779
---------------------------------------------------------------------------------

. eststo margin1: margins, dydx(*) atmeans  post

Conditional marginal effects                    Number of obs     =      2,560
Model VCE    : Robust

Expression   : Pr(Voting), predict()
dy/dx w.r.t. : Treatment TaskPerformance Period Age Men 2.Major 3.Major 5.Major 6.Major CRTScore Competitiveness
at           : Treatment       =          .5 (mean)
               TaskPerfor~e    =      13.375 (mean)
               Period          =        20.5 (mean)
               Age             =    20.10938 (mean)
               Men             =       .3125 (mean)
               1.Major         =         .25 (mean)
               2.Major         =      .21875 (mean)
               3.Major         =     .109375 (mean)
               5.Major         =     .109375 (mean)
               6.Major         =       .3125 (mean)
               CRTScore        =     .453125 (mean)
               Competitiv~s    =    6.296875 (mean)

---------------------------------------------------------------------------------
                |            Delta-method
                |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      Treatment |   .1319472   .0555214     2.38   0.017     .0231273    .2407671
TaskPerformance |   .0155548   .0070781     2.20   0.028      .001682    .0294275
         Period |  -.0004949   .0029319    -0.17   0.866    -.0062412    .0052515
            Age |  -.0027904   .0117192    -0.24   0.812    -.0257595    .0201787
            Men |   .1516164   .0533553     2.84   0.004      .047042    .2561909
                |
          Major |
             2  |   .0110008   .0905369     0.12   0.903    -.1664481    .1884498
             3  |  -.0086375   .0685978    -0.13   0.900    -.1430867    .1258118
             5  |    -.06808   .0821209    -0.83   0.407     -.229034    .0928741
             6  |  -.0806134   .0593601    -1.36   0.174    -.1969572    .0357303
                |
       CRTScore |  -.0518167   .0659574    -0.79   0.432    -.1810908    .0774575
Competitiveness |  -.0106631   .0107377    -0.99   0.321    -.0317086    .0103824
---------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. estimates store m1, title(Model 1)

. logit Voting VG1 TaskPerformance Period Age Men i.Major CRTScore Competitiveness if GroupA==1,vce(cluster UniqueElectorateID)

Iteration 0:   log pseudolikelihood =  -1711.816  
Iteration 1:   log pseudolikelihood = -1442.3358  
Iteration 2:   log pseudolikelihood = -1437.6401  
Iteration 3:   log pseudolikelihood =  -1437.622  
Iteration 4:   log pseudolikelihood =  -1437.622  

Logistic regression                             Number of obs     =      2,560
                                                Wald chi2(11)     =     143.81
                                                Prob > chi2       =     0.0000
Log pseudolikelihood =  -1437.622               Pseudo R2         =     0.1602

                       (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
---------------------------------------------------------------------------------
                |               Robust
         Voting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
            VG1 |   1.569465   .1730952     9.07   0.000     1.230204    1.908725
TaskPerformance |   .1092655   .0266707     4.10   0.000     .0569918    .1615392
         Period |  -.0015682   .0074302    -0.21   0.833     -.016131    .0129947
            Age |  -.0306636   .0517226    -0.59   0.553    -.1320382    .0707109
            Men |   .6389681   .2523835     2.53   0.011     .1443056    1.133631
                |
          Major |
             2  |   .1257995   .4672394     0.27   0.788    -.7899729    1.041572
             3  |    .174682   .3206003     0.54   0.586     -.453683    .8030469
             5  |  -.3846307   .4762312    -0.81   0.419    -1.318027    .5487652
             6  |  -.2875504    .307516    -0.94   0.350    -.8902707    .3151699
                |
       CRTScore |  -.3717255   .3396854    -1.09   0.274    -1.037497    .2940457
Competitiveness |  -.0174323   .0537505    -0.32   0.746    -.1227814    .0879167
          _cons |  -2.000065   1.175496    -1.70   0.089    -4.303994    .3038635
---------------------------------------------------------------------------------

. eststo margin2: margins,  dydx(*) atmeans  post

Conditional marginal effects                    Number of obs     =      2,560
Model VCE    : Robust

Expression   : Pr(Voting), predict()
dy/dx w.r.t. : VG1 TaskPerformance Period Age Men 2.Major 3.Major 5.Major 6.Major CRTScore Competitiveness
at           : VG1             =          .5 (mean)
               TaskPerfor~e    =      13.375 (mean)
               Period          =        20.5 (mean)
               Age             =    20.10938 (mean)
               Men             =       .3125 (mean)
               1.Major         =         .25 (mean)
               2.Major         =      .21875 (mean)
               3.Major         =     .109375 (mean)
               5.Major         =     .109375 (mean)
               6.Major         =       .3125 (mean)
               CRTScore        =     .453125 (mean)
               Competitiv~s    =    6.296875 (mean)

---------------------------------------------------------------------------------
                |            Delta-method
                |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
            VG1 |   .3624951   .0372919     9.72   0.000     .2894045    .4355858
TaskPerformance |   .0252368   .0062419     4.04   0.000     .0130028    .0374707
         Period |  -.0003622   .0017157    -0.21   0.833     -.003725    .0030006
            Age |  -.0070823   .0119548    -0.59   0.554    -.0305132    .0163486
            Men |   .1475808    .058435     2.53   0.012     .0330503    .2621113
                |
          Major |
             2  |   .0301046   .1123252     0.27   0.789    -.1900489     .250258
             3  |    .041996   .0771974     0.54   0.586    -.1093082    .1933001
             5  |  -.0858459   .1021553    -0.84   0.401    -.2860667    .1143749
             6  |  -.0652191   .0703629    -0.93   0.354    -.2031279    .0726897
                |
       CRTScore |  -.0858565   .0776983    -1.10   0.269    -.2381423    .0664293
Competitiveness |  -.0040263   .0124226    -0.32   0.746    -.0283741    .0203215
---------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. estimates store m2, title(Model 2)

. logit Voting Treatment VG1 TreatmentVG1 TaskPerformance Period Age Men i.Major CRTScore Competitiveness if GroupA==1,vce(clust
> er UniqueElectorateID)

Iteration 0:   log pseudolikelihood =  -1711.816  
Iteration 1:   log pseudolikelihood = -1426.0553  
Iteration 2:   log pseudolikelihood =  -1418.118  
Iteration 3:   log pseudolikelihood = -1418.0946  
Iteration 4:   log pseudolikelihood = -1418.0946  

Logistic regression                             Number of obs     =      2,560
                                                Wald chi2(13)     =     124.07
                                                Prob > chi2       =     0.0000
Log pseudolikelihood = -1418.0946               Pseudo R2         =     0.1716

                       (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
---------------------------------------------------------------------------------
                |               Robust
         Voting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      Treatment |   .9922887   .4576963     2.17   0.030     .0952206    1.889357
            VG1 |   1.930782   .3474525     5.56   0.000     1.249787    2.611776
   TreatmentVG1 |  -.5805321   .3900607    -1.49   0.137    -1.345037    .1839728
TaskPerformance |   .0754015   .0334055     2.26   0.024     .0099279    .1408752
         Period |  -.0009987   .0074701    -0.13   0.894    -.0156398    .0136424
            Age |  -.0116099   .0558306    -0.21   0.835     -.121036    .0978161
            Men |   .7365443   .2684137     2.74   0.006     .2104632    1.262625
                |
          Major |
             2  |   .0413002   .4262345     0.10   0.923     -.794104    .8767044
             3  |  -.0433849   .3267218    -0.13   0.894    -.6837479    .5969781
             5  |  -.3335515   .4123017    -0.81   0.419    -1.141648    .4745449
             6  |  -.4030958   .2913451    -1.38   0.166    -.9741216    .1679301
                |
       CRTScore |  -.2385024   .3224013    -0.74   0.459    -.8703973    .3933926
Competitiveness |  -.0495158   .0523508    -0.95   0.344    -.1521214    .0530898
          _cons |  -2.324559    1.25622    -1.85   0.064    -4.786704    .1375859
---------------------------------------------------------------------------------

. eststo margin3: margins,  dydx(*) atmeans  post

Conditional marginal effects                    Number of obs     =      2,560
Model VCE    : Robust

Expression   : Pr(Voting), predict()
dy/dx w.r.t. : Treatment VG1 TreatmentVG1 TaskPerformance Period Age Men 2.Major 3.Major 5.Major 6.Major CRTScore
               Competitiveness
at           : Treatment       =          .5 (mean)
               VG1             =          .5 (mean)
               TreatmentVG1    =         .25 (mean)
               TaskPerfor~e    =      13.375 (mean)
               Period          =        20.5 (mean)
               Age             =    20.10938 (mean)
               Men             =       .3125 (mean)
               1.Major         =         .25 (mean)
               2.Major         =      .21875 (mean)
               3.Major         =     .109375 (mean)
               5.Major         =     .109375 (mean)
               6.Major         =       .3125 (mean)
               CRTScore        =     .453125 (mean)
               Competitiv~s    =    6.296875 (mean)

---------------------------------------------------------------------------------
                |            Delta-method
                |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      Treatment |   .2269234   .1009507     2.25   0.025     .0290637     .424783
            VG1 |   .4415444   .0727761     6.07   0.000     .2989058    .5841829
   TreatmentVG1 |  -.1327601   .0874709    -1.52   0.129    -.3041999    .0386798
TaskPerformance |   .0172433   .0078205     2.20   0.027     .0019155    .0325712
         Period |  -.0002284   .0017067    -0.13   0.894    -.0035735    .0031167
            Age |   -.002655   .0127719    -0.21   0.835    -.0276875    .0223774
            Men |    .168438   .0599531     2.81   0.005     .0509321    .2859439
                |
          Major |
             2  |    .009877   .1020627     0.10   0.923    -.1901621    .2099162
             3  |  -.0102801   .0772745    -0.13   0.894    -.1617353    .1411751
             5  |  -.0759561   .0917627    -0.83   0.408    -.2558077    .1038955
             6  |  -.0907655    .066519    -1.36   0.172    -.2211402    .0396093
                |
       CRTScore |  -.0545423   .0730204    -0.75   0.455    -.1976597     .088575
Competitiveness |  -.0113236   .0119141    -0.95   0.342    -.0346748    .0120276
---------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. estimates store m3, title(Model 3)

. logit Voting Treatment TaskPerformance Period Age Men i.Major CRTScore Competitiveness if GroupA==0,vce(cluster UniqueElectora
> teID)

Iteration 0:   log pseudolikelihood = -2565.9234  
Iteration 1:   log pseudolikelihood = -2408.1736  
Iteration 2:   log pseudolikelihood = -2406.8129  
Iteration 3:   log pseudolikelihood = -2406.8128  

Logistic regression                             Number of obs     =      3,840
                                                Wald chi2(11)     =      26.47
                                                Prob > chi2       =     0.0055
Log pseudolikelihood = -2406.8128               Pseudo R2         =     0.0620

                       (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
---------------------------------------------------------------------------------
                |               Robust
         Voting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      Treatment |    .939528   .2485375     3.78   0.000     .4524034    1.426653
TaskPerformance |   .0620736   .0249312     2.49   0.013     .0132093    .1109379
         Period |  -.0108928   .0061864    -1.76   0.078    -.0230179    .0012323
            Age |  -.0106928   .0335929    -0.32   0.750    -.0765337     .055148
            Men |   .3300808   .1963375     1.68   0.093    -.0547335    .7148952
                |
          Major |
             2  |   .6015688   .3143973     1.91   0.056    -.0146386    1.217776
             3  |   -.063017   .3390498    -0.19   0.853    -.7275424    .6015084
             5  |   .2223041   .4103366     0.54   0.588    -.5819409    1.026549
             6  |   .3042727   .3037855     1.00   0.317     -.291136    .8996813
                |
       CRTScore |  -.0198453    .270085    -0.07   0.941    -.5492023    .5095116
Competitiveness |  -.0677424   .0416982    -1.62   0.104    -.1494693    .0139846
          _cons |  -1.135575   .8615933    -1.32   0.188    -2.824267    .5531169
---------------------------------------------------------------------------------

. eststo margin4: margins, dydx(*) atmeans  post

Conditional marginal effects                    Number of obs     =      3,840
Model VCE    : Robust

Expression   : Pr(Voting), predict()
dy/dx w.r.t. : Treatment TaskPerformance Period Age Men 2.Major 3.Major 5.Major 6.Major CRTScore Competitiveness
at           : Treatment       =          .5 (mean)
               TaskPerfor~e    =    10.07292 (mean)
               Period          =        20.5 (mean)
               Age             =    20.51042 (mean)
               Men             =    .4479167 (mean)
               1.Major         =    .2083333 (mean)
               2.Major         =      .28125 (mean)
               3.Major         =      .09375 (mean)
               5.Major         =    .0833333 (mean)
               6.Major         =    .3333333 (mean)
               CRTScore        =    .3819445 (mean)
               Competitiv~s    =    6.427083 (mean)

---------------------------------------------------------------------------------
                |            Delta-method
                |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      Treatment |   .2210592   .0557126     3.97   0.000     .1118644     .330254
TaskPerformance |   .0146051   .0058651     2.49   0.013     .0031097    .0261006
         Period |  -.0025629   .0014402    -1.78   0.075    -.0053856    .0002598
            Age |  -.0025159   .0078908    -0.32   0.750    -.0179816    .0129498
            Men |   .0776639   .0461316     1.68   0.092    -.0127524    .1680801
                |
          Major |
             2  |    .141246   .0711487     1.99   0.047     .0017972    .2806948
             3  |   -.013429   .0722541    -0.19   0.853    -.1550445    .1281865
             5  |   .0497883   .0922275     0.54   0.589    -.1309743     .230551
             6  |   .0689775   .0675743     1.02   0.307    -.0634658    .2014207
                |
       CRTScore |  -.0046694   .0635725    -0.07   0.941    -.1292691    .1199304
Competitiveness |  -.0159389   .0097453    -1.64   0.102    -.0350394    .0031616
---------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. estimates store m4, title(Model 4)

. logit Voting VG1 TaskPerformance Period Age Men i.Major CRTScore Competitiveness if GroupA==0,vce(cluster UniqueElectorateID)

Iteration 0:   log pseudolikelihood = -2565.9234  
Iteration 1:   log pseudolikelihood = -2467.5714  
Iteration 2:   log pseudolikelihood = -2467.0344  
Iteration 3:   log pseudolikelihood = -2467.0343  

Logistic regression                             Number of obs     =      3,840
                                                Wald chi2(11)     =      45.85
                                                Prob > chi2       =     0.0000
Log pseudolikelihood = -2467.0343               Pseudo R2         =     0.0385

                       (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
---------------------------------------------------------------------------------
                |               Robust
         Voting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
            VG1 |   -.483609   .1103299    -4.38   0.000    -.6998517   -.2673664
TaskPerformance |   .0594047   .0233572     2.54   0.011     .0136253     .105184
         Period |  -.0105716   .0050559    -2.09   0.037    -.0204809   -.0006622
            Age |  -.0252198   .0410021    -0.62   0.538    -.1055824    .0551429
            Men |   .3850321    .217926     1.77   0.077    -.0420951    .8121593
                |
          Major |
             2  |   .3788578   .3261133     1.16   0.245    -.2603125    1.018028
             3  |   .0970649    .419491     0.23   0.817    -.7251224    .9192523
             5  |   .1636766   .4048816     0.40   0.686    -.6298768      .95723
             6  |   .2143098   .3135051     0.68   0.494    -.4001488    .8287685
                |
       CRTScore |  -.1524899   .3487748    -0.44   0.662     -.836076    .5310962
Competitiveness |  -.0894038   .0445023    -2.01   0.045    -.1766267   -.0021809
          _cons |   .1587096   .9767095     0.16   0.871    -1.755606    2.073025
---------------------------------------------------------------------------------

. eststo margin5: margins,  dydx(*) atmeans  post

Conditional marginal effects                    Number of obs     =      3,840
Model VCE    : Robust

Expression   : Pr(Voting), predict()
dy/dx w.r.t. : VG1 TaskPerformance Period Age Men 2.Major 3.Major 5.Major 6.Major CRTScore Competitiveness
at           : VG1             =          .5 (mean)
               TaskPerfor~e    =    10.07292 (mean)
               Period          =        20.5 (mean)
               Age             =    20.51042 (mean)
               Men             =    .4479167 (mean)
               1.Major         =    .2083333 (mean)
               2.Major         =      .28125 (mean)
               3.Major         =      .09375 (mean)
               5.Major         =    .0833333 (mean)
               6.Major         =    .3333333 (mean)
               CRTScore        =    .3819445 (mean)
               Competitiv~s    =    6.427083 (mean)

---------------------------------------------------------------------------------
                |            Delta-method
                |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
            VG1 |  -.1142413   .0258675    -4.42   0.000    -.1649406   -.0635421
TaskPerformance |    .014033   .0055235     2.54   0.011     .0032071    .0248588
         Period |  -.0024973    .001156    -2.16   0.031    -.0047629   -.0002316
            Age |  -.0059576   .0096197    -0.62   0.536    -.0248118    .0128967
            Men |   .0909548    .052241     1.74   0.082    -.0114357    .1933454
                |
          Major |
             2  |   .0890363   .0747377     1.19   0.234    -.0574468    .2355195
             3  |   .0220023   .0950955     0.23   0.817    -.1643814    .2083861
             5  |    .037461   .0928098     0.40   0.686    -.1444429    .2193648
             6  |    .049388   .0715588     0.69   0.490    -.0908645    .1896406
                |
       CRTScore |  -.0360222   .0826387    -0.44   0.663    -.1979911    .1259467
Competitiveness |  -.0211196   .0103525    -2.04   0.041      -.04141   -.0008291
---------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. estimates store m5, title(Model 5)

. logit Voting Treatment VG1 TreatmentVG1 TaskPerformance Period Age Men i.Major CRTScore Competitiveness if GroupA==0,vce(clust
> er UniqueElectorateID)

Iteration 0:   log pseudolikelihood = -2565.9234  
Iteration 1:   log pseudolikelihood = -2381.2199  
Iteration 2:   log pseudolikelihood = -2379.5267  
Iteration 3:   log pseudolikelihood = -2379.5265  

Logistic regression                             Number of obs     =      3,840
                                                Wald chi2(13)     =      53.76
                                                Prob > chi2       =     0.0000
Log pseudolikelihood = -2379.5265               Pseudo R2         =     0.0726

                       (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
---------------------------------------------------------------------------------
                |               Robust
         Voting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      Treatment |   .8736181    .262755     3.32   0.001     .3586279    1.388608
            VG1 |  -.5986825   .1552789    -3.86   0.000    -.9030235   -.2943415
   TreatmentVG1 |    .168424   .2280882     0.74   0.460    -.2786208    .6154687
TaskPerformance |   .0630671   .0252493     2.50   0.012     .0135794    .1125549
         Period |  -.0109772   .0053381    -2.06   0.040    -.0214397   -.0005148
            Age |  -.0116209   .0341901    -0.34   0.734    -.0786324    .0553905
            Men |   .3365484   .1984619     1.70   0.090    -.0524298    .7255265
                |
          Major |
             2  |   .6066862   .3175125     1.91   0.056    -.0156269    1.228999
             3  |  -.0666615   .3427147    -0.19   0.846      -.73837    .6050471
             5  |   .2132457   .4169322     0.51   0.609    -.6039263    1.030418
             6  |   .3059373   .3068832     1.00   0.319    -.2955427    .9074173
                |
       CRTScore |  -.0190156   .2726912    -0.07   0.944    -.5534806    .5154494
Competitiveness |  -.0686159   .0422157    -1.63   0.104    -.1513572    .0141254
          _cons |   -.842568   .8929061    -0.94   0.345    -2.592632    .9074957
---------------------------------------------------------------------------------

. eststo margin6: margins,  dydx(*) atmeans  post

Conditional marginal effects                    Number of obs     =      3,840
Model VCE    : Robust

Expression   : Pr(Voting), predict()
dy/dx w.r.t. : Treatment VG1 TreatmentVG1 TaskPerformance Period Age Men 2.Major 3.Major 5.Major 6.Major CRTScore
               Competitiveness
at           : Treatment       =          .5 (mean)
               VG1             =          .5 (mean)
               TreatmentVG1    =         .25 (mean)
               TaskPerfor~e    =    10.07292 (mean)
               Period          =        20.5 (mean)
               Age             =    20.51042 (mean)
               Men             =    .4479167 (mean)
               1.Major         =    .2083333 (mean)
               2.Major         =      .28125 (mean)
               3.Major         =      .09375 (mean)
               5.Major         =    .0833333 (mean)
               6.Major         =    .3333333 (mean)
               CRTScore        =    .3819445 (mean)
               Competitiv~s    =    6.427083 (mean)

---------------------------------------------------------------------------------
                |            Delta-method
                |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      Treatment |   .2050767   .0592768     3.46   0.001     .0888963    .3212571
            VG1 |  -.1405372   .0361035    -3.89   0.000    -.2112986   -.0697757
   TreatmentVG1 |   .0395365   .0534764     0.74   0.460    -.0652754    .1443484
TaskPerformance |   .0148046   .0059281     2.50   0.013     .0031858    .0264234
         Period |  -.0025768    .001216    -2.12   0.034    -.0049601   -.0001936
            Age |  -.0027279   .0080091    -0.34   0.733    -.0184254    .0129695
            Men |   .0790027   .0465036     1.70   0.089    -.0121427    .1701482
                |
          Major |
             2  |   .1421764   .0716929     1.98   0.047     .0016608    .2826919
             3  |  -.0141389   .0726896    -0.19   0.846    -.1566079    .1283301
             5  |   .0475325   .0933315     0.51   0.611    -.1353938    .2304589
             6  |   .0691537   .0680771     1.02   0.310     -.064275    .2025824
                |
       CRTScore |  -.0044638   .0640355    -0.07   0.944    -.1299711    .1210435
Competitiveness |  -.0161072   .0098401    -1.64   0.102    -.0353934    .0031791
---------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. estimates store m6, title(Model 6)

. 
. esttab margin1 margin2 margin3 margin4 margin5 margin6 using Table2.txt,cells(b(star fmt(3)) se(par fmt(3))) star(* 0.10 ** 0.
> 05 *** 0.01) stats(r2_a N,fmt(%9.3f %9.0g)) order(Treatment VG1 TreatmentVG1 TaskPerformance Period Age Men CRTScore Competiti
> veness) legend label collabels(none) replace
(note: file Table2.txt not found)
(output written to Table2.txt)

. ////////////////////////////////////////////////////////////////////////////////
> ////Note: The complete table of results is reported in Table A4 of Appendix E///
> ////////////////////////////////////////////////////////////////////////////////
> 
. 
. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////         Analysis of Otherparty Voting (Appendix D)        /////////////
> gen OtherpartyVoting=0

. replace OtherpartyVoting=1 if GroupA==1&Vote==2
(69 real changes made)

. replace OtherpartyVoting=1 if GroupA==0&Vote==1
(56 real changes made)

. 
. summarize OtherpartyVoting if Treatment==0&GroupA==1&VotingGame==1

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
Otherparty~g |        640     .015625    .1241166          0          1

. summarize OtherpartyVoting if Treatment==1&GroupA==1&VotingGame==1

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
Otherparty~g |        640       .0125    .1111893          0          1

. summarize OtherpartyVoting if Treatment==0&GroupA==1&VotingGame==2

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
Otherparty~g |        640       .0625    .2422508          0          1

. summarize OtherpartyVoting if Treatment==1&GroupA==1&VotingGame==2

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
Otherparty~g |        640    .0171875    .1300712          0          1

. summarize OtherpartyVoting if Treatment==0&GroupA==0&VotingGame==1

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
Otherparty~g |        960    .0166667    .1280858          0          1

. summarize OtherpartyVoting if Treatment==1&GroupA==0&VotingGame==1

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
Otherparty~g |        960    .0145833    .1199402          0          1

. summarize OtherpartyVoting if Treatment==0&GroupA==0&VotingGame==2

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
Otherparty~g |        960     .015625    .1240842          0          1

. summarize OtherpartyVoting if Treatment==1&GroupA==0&VotingGame==2

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
Otherparty~g |        960    .0114583     .106484          0          1

. 
. logit OtherpartyVoting Treatment if GroupA==1&VotingGame==1,vce(cluster UniqueElectorateID)

Iteration 0:   log pseudolikelihood = -94.629225  
Iteration 1:   log pseudolikelihood = -94.516638  
Iteration 2:   log pseudolikelihood = -94.516299  
Iteration 3:   log pseudolikelihood = -94.516299  

Logistic regression                             Number of obs     =      1,280
                                                Wald chi2(1)      =       0.18
                                                Prob > chi2       =     0.6746
Log pseudolikelihood = -94.516299               Pseudo R2         =     0.0012

                        (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
----------------------------------------------------------------------------------
                 |               Robust
OtherpartyVoting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
       Treatment |  -.2263131   .5390462    -0.42   0.675    -1.282824    .8301981
           _cons |  -4.143135   .3537957   -11.71   0.000    -4.836561   -3.449708
----------------------------------------------------------------------------------

. logit OtherpartyVoting Treatment if GroupA==1&VotingGame==2,vce(cluster UniqueElectorateID)

Iteration 0:   log pseudolikelihood = -214.33249  
Iteration 1:   log pseudolikelihood = -205.93867  
Iteration 2:   log pseudolikelihood = -205.23218  
Iteration 3:   log pseudolikelihood = -205.23089  
Iteration 4:   log pseudolikelihood = -205.23089  

Logistic regression                             Number of obs     =      1,280
                                                Wald chi2(1)      =       6.82
                                                Prob > chi2       =     0.0090
Log pseudolikelihood = -205.23089               Pseudo R2         =     0.0425

                        (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
----------------------------------------------------------------------------------
                 |               Robust
OtherpartyVoting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
       Treatment |  -1.338186   .5124923    -2.61   0.009    -2.342652   -.3337194
           _cons |   -2.70805    .329605    -8.22   0.000    -3.354064   -2.062036
----------------------------------------------------------------------------------

. logit OtherpartyVoting Treatment if GroupA==0&VotingGame==1,vce(cluster UniqueElectorateID)

Iteration 0:   log pseudolikelihood = -154.53089  
Iteration 1:   log pseudolikelihood = -154.46319  
Iteration 2:   log pseudolikelihood = -154.46311  
Iteration 3:   log pseudolikelihood = -154.46311  

Logistic regression                             Number of obs     =      1,920
                                                Wald chi2(1)      =       0.08
                                                Prob > chi2       =     0.7810
Log pseudolikelihood = -154.46311               Pseudo R2         =     0.0004

                        (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
----------------------------------------------------------------------------------
                 |               Robust
OtherpartyVoting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
       Treatment |  -.1356478   .4879072    -0.28   0.781    -1.091928    .8206328
           _cons |  -4.077537   .3765415   -10.83   0.000    -4.815545    -3.33953
----------------------------------------------------------------------------------

. logit OtherpartyVoting Treatment if GroupA==0&VotingGame==2,vce(cluster UniqueElectorateID)

Iteration 0:   log pseudolikelihood = -137.67474  
Iteration 1:   log pseudolikelihood = -137.36341  
Iteration 2:   log pseudolikelihood =  -137.3616  
Iteration 3:   log pseudolikelihood =  -137.3616  

Logistic regression                             Number of obs     =      1,920
                                                Wald chi2(1)      =       0.34
                                                Prob > chi2       =     0.5578
Log pseudolikelihood =  -137.3616               Pseudo R2         =     0.0023

                        (Std. Err. adjusted for 32 clusters in UniqueElectorateID)
----------------------------------------------------------------------------------
                 |               Robust
OtherpartyVoting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
       Treatment |  -.3143788   .5364311    -0.59   0.558    -1.365764    .7370068
           _cons |  -4.143135   .3436123   -12.06   0.000    -4.816603   -3.469667
----------------------------------------------------------------------------------

. 
. 
. sort UniqueGroupIDbyElectorate

. ///Group A's OtherpartyVoting in VG2 of Treatment Group///
> by UniqueGroupIDbyElectorate: egen AVG2TreatmentO=mean(OtherpartyVoting) if GroupA==1&VotingGame==2&Treatment==1
(5760 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupAVG2TreatmentO=mean(AVG2TreatmentO)
(5120 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupAVG2TreatmentOAvg=GroupAVG2TreatmentO if _n==2
(6,384 missing values generated)

. 
. ///Group A's OtherpartyVoting in VG2 of Control Group///
> by UniqueGroupIDbyElectorate: egen AVG2ControlO=mean(OtherpartyVoting) if GroupA==1&VotingGame==2&Treatment==0
(5760 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupAVG2ControlO=mean(AVG2ControlO)
(5120 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupAVG2ControlOAvg=GroupAVG2ControlO if _n==2
(6,384 missing values generated)

. 
. ///Comparisons of Group A's OtherpartyVoting in VG2 Across Treatments/// Appendix D
> gen AVG2OtherVotingAcrossTreatments=GroupAVG2TreatmentOAvg if Treatment==1
(6,384 missing values generated)

. replace AVG2OtherVotingAcrossTreatments=GroupAVG2ControlOAvg if Treatment==0
(16 real changes made)

. 
. ttest AVG2OtherVotingAcrossTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16       .0625     .019632    .0785281    .0206553    .1043447
       1 |      16    .0171875    .0067387    .0269548    .0028243    .0315507
---------+--------------------------------------------------------------------
combined |      32    .0398438    .0109905    .0621715    .0174285     .062259
---------+--------------------------------------------------------------------
    diff |            .0453125    .0207564                .0029223    .0877027
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   2.1831
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9815         Pr(|T| > |t|) = 0.0370          Pr(T > t) = 0.0185

. ranksum AVG2OtherVotingAcrossTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16         315         264
           1 |       16         213         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties      -70.58
                     ----------
adjusted variance        633.42

Ho: AVG2Ot~s(Treatm~t==0) = AVG2Ot~s(Treatm~t==1)
             z =   2.026
    Prob > |z| =   0.0427

. restore

. 
. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ********************************************************************************
. *                                                                              *
. *                     Statistical Analysis of Experiment II                    *
. *                                                                              *
. ********************************************************************************
. //As noted in the paper, the results of Experiment II are reported in Online Appendix F//
. //Again, in Exp II, subjects rarely voted for the policy preferred by the other group and most of such other party voting happ
> ened in the first few periods//
. //Whether including voting for the policy preferred by the other group or not does not change our conclusions//
. 
. preserve

. keep if Experiment==2
(9,700 observations deleted)

. ///Generate Electorate Average of Group A Voters' Voting by Voting Game and Treatment///
> ///Group A's Voting in VG1 of Treatment Group///
> sort UniqueGroupIDbyElectorate

. by UniqueGroupIDbyElectorate: egen AVG1Treatment=mean(Voting) if GroupA==1&VotingGame==1&Treatment==1
(5760 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupAVG1Treatment=mean(AVG1Treatment)
(5120 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupAVG1TreatmentAvg=GroupAVG1Treatment if _n==1
(6,384 missing values generated)

. ///Group A's Voting in VG2 of Treatment Group///
> by UniqueGroupIDbyElectorate: egen AVG2Treatment=mean(Voting) if GroupA==1&VotingGame==2&Treatment==1
(5760 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupAVG2Treatment=mean(AVG2Treatment)
(5120 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupAVG2TreatmentAvg=GroupAVG2Treatment if _n==2
(6,384 missing values generated)

. ///Group A's Voting in VG1 of Control Group///
> sort UniqueGroupIDbyElectorate

. by UniqueGroupIDbyElectorate: egen AVG1Control=mean(Voting) if GroupA==1&VotingGame==1&Treatment==0
(5760 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupAVG1Control=mean(AVG1Control)
(5120 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupAVG1ControlAvg=GroupAVG1Control if _n==1
(6,384 missing values generated)

. ///Group A's Voting in VG2 of Control Group///
> by UniqueGroupIDbyElectorate: egen AVG2Control=mean(Voting) if GroupA==1&VotingGame==2&Treatment==0
(5760 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupAVG2Control=mean(AVG2Control)
(5120 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupAVG2ControlAvg=GroupAVG2Control if _n==2
(6,384 missing values generated)

. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ///Group B's Voting in VG1 of Treatment Group///
> sort UniqueGroupIDbyElectorate

. by UniqueGroupIDbyElectorate: egen BVG1Treatment=mean(Voting) if GroupA==0&VotingGame==1&Treatment==1
(5440 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupBVG1Treatment=mean(BVG1Treatment)
(4480 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupBVG1TreatmentAvg=GroupBVG1Treatment if _n==1
(6,384 missing values generated)

. ///Group B's Voting in VG2 of Treatment Group///
> by UniqueGroupIDbyElectorate: egen BVG2Treatment=mean(Voting) if GroupA==0&VotingGame==2&Treatment==1
(5440 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupBVG2Treatment=mean(BVG2Treatment)
(4480 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupBVG2TreatmentAvg=GroupBVG2Treatment if _n==2
(6,384 missing values generated)

. ///Group B's Voting in VG1 of Control Group///
> sort UniqueGroupIDbyElectorate

. by UniqueGroupIDbyElectorate: egen BVG1Control=mean(Voting) if GroupA==0&VotingGame==1&Treatment==0
(5440 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupBVG1Control=mean(BVG1Control)
(4480 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupBVG1ControlAvg=GroupBVG1Control if _n==1
(6,384 missing values generated)

. ///Group B's Voting in VG2 of Control Group///
> by UniqueGroupIDbyElectorate: egen BVG2Control=mean(Voting) if GroupA==0&VotingGame==2&Treatment==0
(5440 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupBVG2Control=mean(BVG2Control)
(4480 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupBVG2ControlAvg=GroupBVG2Control if _n==2
(6,384 missing values generated)

. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ///Group A voters, in VG1, voted about 43% of the time in the Control and 44% in the Treatment
> ///and in VG2, voted about 9% of the time in the Control and 12% in the Treatment. 
> ///Group B voters, in VG1 (VG2), voted about 44% (39%) of the time in the Control 
> ///and 41% (39%) in the Treatment condition.
> 
. ///None of these pairwise comparisons are statistically different at the 5% level. 
> 
. 
. ///Comparisons of Group A's Voting in VG1 Across Treatments/// 
> gen AVG1AcrossTreatments=GroupAVG1TreatmentAvg if Treatment==1
(6,384 missing values generated)

. replace AVG1AcrossTreatments=GroupAVG1ControlAvg if Treatment==0
(16 real changes made)

. 
. *ttest Voting if GroupA==1&VotingGame==1,by(Treatment)
. ttest AVG1AcrossTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16     .428125      .05714    .2285598    .3063341    .5499159
       1 |      16    .4421875    .0694742    .2778967    .2941068    .5902682
---------+--------------------------------------------------------------------
combined |      32    .4351562    .0442634    .2503916    .3448805     .525432
---------+--------------------------------------------------------------------
    diff |           -.0140625    .0899535               -.1977721    .1696471
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -0.1563
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.4384         Pr(|T| > |t|) = 0.8768          Pr(T > t) = 0.5616

. ranksum AVG1AcrossTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16         254         264
           1 |       16         274         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -2.19
                     ----------
adjusted variance        701.81

Ho: AVG1Ac~s(Treatm~t==0) = AVG1Ac~s(Treatm~t==1)
             z =  -0.377
    Prob > |z| =   0.7058

. 
. ///Comparisons of Group B's Voting in VG1 Across Treatments/// 
> gen BVG1AcrossTreatments=GroupBVG1TreatmentAvg if Treatment==1
(6,384 missing values generated)

. replace BVG1AcrossTreatments=GroupBVG1ControlAvg if Treatment==0
(16 real changes made)

. 
. *ttest Voting if GroupA==0&VotingGame==1,by(Treatment)
. ttest BVG1AcrossTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16     .446875    .0458262    .1833049    .3491987    .5445513
       1 |      16    .4052083    .0617589    .2470357    .2735723    .5368443
---------+--------------------------------------------------------------------
combined |      32    .4260417    .0380113    .2150243    .3485171    .5035662
---------+--------------------------------------------------------------------
    diff |            .0416667    .0769039                -.115392    .1987253
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   0.5418
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.7040         Pr(|T| > |t|) = 0.5920          Pr(T > t) = 0.2960

. ranksum BVG1AcrossTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16       268.5         264
           1 |       16       259.5         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -3.35
                     ----------
adjusted variance        700.65

Ho: BVG1Ac~s(Treatm~t==0) = BVG1Ac~s(Treatm~t==1)
             z =   0.170
    Prob > |z| =   0.8650

. 
. ///Comparisons of Group A's Voting in VG2 Across Treatments/// 
> gen AVG2AcrossTreatments=GroupAVG2TreatmentAvg if Treatment==1
(6,384 missing values generated)

. replace AVG2AcrossTreatments=GroupAVG2ControlAvg if Treatment==0
(16 real changes made)

. 
. *ttest Voting if GroupA==1&VotingGame==2,by(Treatment)
. ttest AVG2AcrossTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16      .09375    .0350223    .1400893    .0191017    .1683983
       1 |      16    .1234375    .0407909    .1631637    .0364937    .2103813
---------+--------------------------------------------------------------------
combined |      32    .1085937    .0265784    .1503503    .0543867    .1628008
---------+--------------------------------------------------------------------
    diff |           -.0296875     .053763               -.1394862    .0801112
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -0.5522
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.2925         Pr(|T| > |t|) = 0.5849          Pr(T > t) = 0.7075

. ranksum AVG2AcrossTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16         257         264
           1 |       16         271         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties      -31.74
                     ----------
adjusted variance        672.26

Ho: AVG2Ac~s(Treatm~t==0) = AVG2Ac~s(Treatm~t==1)
             z =  -0.270
    Prob > |z| =   0.7872

. 
. ///Comparisons of Group B's Voting in VG2 Across Treatments/// 
> gen BVG2AcrossTreatments=GroupBVG2TreatmentAvg if Treatment==1
(6,384 missing values generated)

. replace BVG2AcrossTreatments=GroupBVG2ControlAvg if Treatment==0
(16 real changes made)

. 
. *ttest Voting if GroupA==0&VotingGame==2,by(Treatment)
. ttest BVG2AcrossTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16    .3927083    .0453374    .1813497    .2960739    .4893428
       1 |      16     .390625    .0543899    .2175596    .2746957    .5065543
---------+--------------------------------------------------------------------
combined |      32    .3916667    .0348287    .1970208    .3206331    .4627002
---------+--------------------------------------------------------------------
    diff |            .0020833    .0708078               -.1425255    .1466921
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   0.0294
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.5116         Pr(|T| > |t|) = 0.9767          Pr(T > t) = 0.4884

. ranksum BVG2AcrossTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16       255.5         264
           1 |       16       272.5         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -2.06
                     ----------
adjusted variance        701.94

Ho: BVG2Ac~s(Treatm~t==0) = BVG2Ac~s(Treatm~t==1)
             z =  -0.321
    Prob > |z| =   0.7483

. restore

. 
. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ///Looking at the self-reported values regarding how important it is for an individual to vote, 
> ///Group A's average is 5.09 in the Control and 4.91 in the Treatment. 
> ///Group B's average is 5.08 in the Control and 5.19 in the Treatment. 
> ///Regarding how important it is for an individual to earn more than the others, 
> ///Group A's average is 5.44 in the Control and 5.19 in the Treatment. Group B's average is 5.48 in the Control and 5.29 in th
> e Treatment. 
> 
. ///None of these pairwise comparisons are statistically different at the 5% level. 
> 
. preserve

. keep if Experiment==2
(9,700 observations deleted)

. keep if Period==40  
(6,240 observations deleted)

. *post-treatment survey was conducted right after the 40th round of voting and was elicited once*
. *generate Electorate Average of Valuations by Group and Treatment*
. sort UniqueElectorateID

. by UniqueElectorateID: egen GroupAValue=mean(VotingImportance) if GroupA==1
(96 missing values generated)

. by UniqueElectorateID, sort: egen AMeanValue=mean(GroupAValue)

. by UniqueElectorateID: gen GroupAMeanValue=AMeanValue if _n==1
(128 missing values generated)

. sort UniqueElectorateID

. by UniqueElectorateID: egen GroupBValue=mean(VotingImportance) if GroupA==0
(64 missing values generated)

. by UniqueElectorateID, sort: egen BMeanValue=mean(GroupBValue)

. by UniqueElectorateID: gen GroupBMeanValue=BMeanValue if _n==1
(128 missing values generated)

. 
. ttest GroupAMeanValue,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16     5.09375    .4383177    1.753271    4.159498    6.028002
       1 |      16     4.90625    .2509098    1.003639    4.371448    5.441052
---------+--------------------------------------------------------------------
combined |      32           5    .2489899      1.4085    4.492182    5.507818
---------+--------------------------------------------------------------------
    diff |               .1875    .5050526                -.843955    1.218955
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   0.3712
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.6435         Pr(|T| > |t|) = 0.7131          Pr(T > t) = 0.3565

. ranksum GroupAMeanValue,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16       256.5         264
           1 |       16       271.5         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties      -20.00
                     ----------
adjusted variance        684.00

Ho: GroupAM~(Treatm~t==0) = GroupAM~(Treatm~t==1)
             z =  -0.287
    Prob > |z| =   0.7743

. 
. ttest GroupBMeanValue,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16    6.083333    .3670453    1.468181    5.300995    6.865672
       1 |      16      5.1875    .3305001       1.322    4.483056    5.891944
---------+--------------------------------------------------------------------
combined |      32    5.635417    .2559154    1.447676    5.113474     6.15736
---------+--------------------------------------------------------------------
    diff |            .8958333    .4939155               -.1128767    1.904543
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   1.8137
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9601         Pr(|T| > |t|) = 0.0797          Pr(T > t) = 0.0399

. ranksum GroupBMeanValue,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16       318.5         264
           1 |       16       209.5         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -5.81
                     ----------
adjusted variance        698.19

Ho: GroupBM~(Treatm~t==0) = GroupBM~(Treatm~t==1)
             z =   2.063
    Prob > |z| =   0.0392

. 
. 
. *generate Electorate Average of Valuations by Group and Treatment*
. sort UniqueElectorateID

. by UniqueElectorateID: egen GroupAStatus=mean(EarningMorethanOthers) if GroupA==1
(96 missing values generated)

. by UniqueElectorateID, sort: egen AMeanStatus=mean(GroupAStatus)

. by UniqueElectorateID: gen GroupAMeanStatus=AMeanStatus if _n==1
(128 missing values generated)

. sort UniqueElectorateID

. by UniqueElectorateID: egen GroupBStatus=mean(EarningMorethanOthers) if GroupA==0
(64 missing values generated)

. by UniqueElectorateID, sort: egen BMeanStatus=mean(GroupBStatus)

. by UniqueElectorateID: gen GroupBMeanStatus=BMeanStatus if _n==1
(128 missing values generated)

. 
. ttest GroupAMeanStatus,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16      5.4375    .4806138    1.922455    4.413096    6.461904
       1 |      16      5.1875    .2494786    .9979145    4.655749    5.719251
---------+--------------------------------------------------------------------
combined |      32      5.3125    .2672949    1.512048    4.767348    5.857652
---------+--------------------------------------------------------------------
    diff |                 .25    .5415064               -.8559036    1.355904
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   0.4617
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.6762         Pr(|T| > |t|) = 0.6476          Pr(T > t) = 0.3238

. ranksum GroupAMeanStatus,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16         265         264
           1 |       16         263         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -9.81
                     ----------
adjusted variance        694.19

Ho: GroupA..(Treatm~t==0) = GroupA..(Treatm~t==1)
             z =   0.038
    Prob > |z| =   0.9697

. 
. ttest GroupBMeanStatus,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16    5.479167    .3042428    1.216971    4.830689    6.127645
       1 |      16    5.291667    .3086335    1.234534     4.63383    5.949503
---------+--------------------------------------------------------------------
combined |      32    5.385417    .2138304    1.209607    4.949307    5.821527
---------+--------------------------------------------------------------------
    diff |               .1875    .4333801               -.6975802     1.07258
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   0.4326
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.6658         Pr(|T| > |t|) = 0.6684          Pr(T > t) = 0.3342

. ranksum GroupBMeanStatus,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16         271         264
           1 |       16         257         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties      -10.58
                     ----------
adjusted variance        693.42

Ho: GroupB..(Treatm~t==0) = GroupB..(Treatm~t==1)
             z =   0.266
    Prob > |z| =   0.7904

. restore

. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> /////////            Examine Voting Outcomes Across Treatments          ////////
> ////////////////////////////////////////////////////////////////////////////////
> *****recall that each Group A voter has 1 ballot in Exp. II*****
. preserve

. keep if Experiment==2
(9,700 observations deleted)

. 
. gen VoteA=0

. replace VoteA=1 if Vote==1&GroupA==1
(696 real changes made)

. replace VoteA=1 if Vote==1&GroupA==0
(88 real changes made)

. gen VoteB=0

. replace VoteB=1 if Vote==2&GroupA==1
(165 real changes made)

. replace VoteB=1 if Vote==2&GroupA==0
(1,570 real changes made)

. 
. *****compute how many votes are for A and B*****
. by UniqueElectionPeriodID, sort: egen V4A=total(VoteA)

. by UniqueElectionPeriodID, sort: egen V4B=total(VoteB)

. 
. 
. sort UniqueElectorateID Period Subject

. 
. gen ProbBWin=0

. replace ProbBWin=0.5 if V4A==0&V4B==0
(1,170 real changes made)

. replace ProbBWin=V4B/(V4A+V4B) if V4A+V4B>0
(4,900 real changes made)

. 
. ***generate electorate average of computed likelihood Policy B Wins in VG1******
. sort UniqueElectorateID

. by UniqueElectorateID: egen ProbBWinVG1=mean(ProbBWin) if VotingGame==1
(3200 missing values generated)

. by UniqueElectorateID, sort: egen ProbBWinVG1Avg=mean(ProbBWinVG1)

. by UniqueElectorateID: gen VG1ProbBWinElectorateLevel=ProbBWinVG1Avg if _n==1
(6,368 missing values generated)

. 
. ***generate electorate average of computed likelihood Policy B Wins in VG2******
. sort UniqueElectorateID

. by UniqueElectorateID: egen ProbBWinVG2=mean(ProbBWin) if VotingGame==2
(3200 missing values generated)

. by UniqueElectorateID, sort: egen ProbBWinVG2Avg=mean(ProbBWinVG2)

. by UniqueElectorateID: gen VG2ProbBWinElectorateLevel=ProbBWinVG2Avg if _n==1
(6,368 missing values generated)

. 
. *compare electorate average of computed likelihood Policy B Wins by Voting Game*
. *ttest ProbBWin if VotingGame==1,by(Treatment)
. ttest VG1ProbBWinElectorateLevel,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16        .585    .0207194    .0828776    .5408376    .6291624
       1 |      16    .5543229    .0286566    .1146263    .4932429     .615403
---------+--------------------------------------------------------------------
combined |      32    .5696615    .0176105    .0996198    .5337447    .6055782
---------+--------------------------------------------------------------------
    diff |            .0306771    .0353623               -.0415424    .1028966
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   0.8675
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.8037         Pr(|T| > |t|) = 0.3926          Pr(T > t) = 0.1963

. ranksum VG1ProbBWinElectorateLevel,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16       304.5         264
           1 |       16       223.5         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -0.65
                     ----------
adjusted variance        703.35

Ho: VG1Pro~l(Treatm~t==0) = VG1Pro~l(Treatm~t==1)
             z =   1.527
    Prob > |z| =   0.1267

. 
. *ttest ProbBWin if VotingGame==2,by(Treatment)
. ttest VG2ProbBWinElectorateLevel,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      16    .7897917     .034057    .1362281    .7172008    .8623825
       1 |      16    .7867708    .0413527    .1654108    .6986296     .874912
---------+--------------------------------------------------------------------
combined |      32    .7882813    .0263517    .1490676    .7345367    .8420258
---------+--------------------------------------------------------------------
    diff |            .0030208    .0535717               -.1063872    .1124288
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =   0.0564
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.5223         Pr(|T| > |t|) = 0.9554          Pr(T > t) = 0.4777

. ranksum VG2ProbBWinElectorateLevel,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       16       260.5         264
           1 |       16       267.5         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -1.29
                     ----------
adjusted variance        702.71

Ho: VG2Pro~l(Treatm~t==0) = VG2Pro~l(Treatm~t==1)
             z =  -0.132
    Prob > |z| =   0.8950

. restore

. 
. 
. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ********************************************************************************
. *                                                                              *
. *      Comparisons between Experiment I and Experiment II (Figure 6)           *
. *                                                                              *
. ********************************************************************************
. preserve

. drop if Experiment==3
(3,300 observations deleted)

. ///Generate Electorate Average of Group A Voters' Voting by Voting Game, Treatment and Experiment///
> 
. sort UniqueGroupIDbyElectorate

. 
. ///Group A's Voting in VG2 of Treatment Group///
> by UniqueGroupIDbyElectorate: egen AVG2Treatment=mean(Voting) if GroupA==1&VotingGame==2&Treatment==1
(11520 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupAVG2Treatment=mean(AVG2Treatment)
(10240 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupAVG2TreatmentAvg=GroupAVG2Treatment if _n==2
(12,768 missing values generated)

. 
. ///Group A's Voting in VG2 of Control Group///
> by UniqueGroupIDbyElectorate: egen AVG2Control=mean(Voting) if GroupA==1&VotingGame==2&Treatment==0
(11520 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupAVG2Control=mean(AVG2Control)
(10240 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupAVG2ControlAvg=GroupAVG2Control if _n==2
(12,768 missing values generated)

. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> 
. ///Group B's Voting in VG2 of Treatment Group///
> by UniqueGroupIDbyElectorate: egen BVG2Treatment=mean(Voting) if GroupA==0&VotingGame==2&Treatment==1
(10880 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupBVG2Treatment=mean(BVG2Treatment)
(8960 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupBVG2TreatmentAvg=GroupBVG2Treatment if _n==2
(12,768 missing values generated)

. 
. ///Group B's Voting in VG2 of Control Group///
> by UniqueGroupIDbyElectorate: egen BVG2Control=mean(Voting) if GroupA==0&VotingGame==2&Treatment==0
(10880 missing values generated)

. by UniqueGroupIDbyElectorate, sort: egen GroupBVG2Control=mean(BVG2Control)
(8960 missing values generated)

. sort UniqueGroupIDbyElectorate Period Subject 

. by UniqueGroupIDbyElectorate: gen GroupBVG2ControlAvg=GroupBVG2Control if _n==2
(12,768 missing values generated)

. 
. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ///  Comparisons of Group A's Voting in VG2 of Treatment Across Experiments  ///
> gen GroupAVG2TreatmentAcrossExps=GroupAVG2TreatmentAvg if Treatment==1&Experiment==1
(12,784 missing values generated)

. replace GroupAVG2TreatmentAcrossExps=GroupAVG2TreatmentAvg if Treatment==1&Experiment==2
(16 real changes made)

. ttest GroupAVG2TreatmentAcrossExps,by(Experiment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       1 |      16     .340625    .0479732     .191893    .2383724    .4428776
       2 |      16    .1234375    .0407909    .1631637    .0364937    .2103813
---------+--------------------------------------------------------------------
combined |      32    .2320313    .0366027    .2070564    .1573795     .306683
---------+--------------------------------------------------------------------
    diff |            .2171875    .0629709                .0885838    .3457912
------------------------------------------------------------------------------
    diff = mean(1) - mean(2)                                      t =   3.4490
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9992         Pr(|T| > |t|) = 0.0017          Pr(T > t) = 0.0008

. ranksum GroupAVG2TreatmentAcrossExps,by(Experiment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

  Experiment |      obs    rank sum    expected
-------------+---------------------------------
           1 |       16         352         264
           2 |       16         176         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -5.68
                     ----------
adjusted variance        698.32

Ho: GroupA~s(Experi~t==1) = GroupA~s(Experi~t==2)
             z =   3.330
    Prob > |z| =   0.0009

. ////////////////////////////////////////////////////////////////////////////////
> ///  Comparisons of Group B's Voting in VG2 of Treatment Across Experiments  ///
> gen GroupBVG2TreatmentAcrossExps=GroupBVG2TreatmentAvg if Treatment==1&Experiment==1
(12,784 missing values generated)

. replace GroupBVG2TreatmentAcrossExps=GroupBVG2TreatmentAvg if Treatment==1&Experiment==2
(16 real changes made)

. ttest GroupBVG2TreatmentAcrossExps,by(Experiment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       1 |      16    .5385417    .0447917    .1791667    .4430705    .6340128
       2 |      16     .390625    .0543899    .2175596    .2746957    .5065543
---------+--------------------------------------------------------------------
combined |      32    .4645833    .0371153     .209956    .3888861    .5402806
---------+--------------------------------------------------------------------
    diff |            .1479167    .0704596                 .004019    .2918143
------------------------------------------------------------------------------
    diff = mean(1) - mean(2)                                      t =   2.0993
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9778         Pr(|T| > |t|) = 0.0443          Pr(T > t) = 0.0222

. ranksum GroupBVG2TreatmentAcrossExps,by(Experiment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

  Experiment |      obs    rank sum    expected
-------------+---------------------------------
           1 |       16         316         264
           2 |       16         212         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -1.55
                     ----------
adjusted variance        702.45

Ho: GroupB~s(Experi~t==1) = GroupB~s(Experi~t==2)
             z =   1.962
    Prob > |z| =   0.0498

. ////////////////////////////////////////////////////////////////////////////////
> ///   Comparisons of Group A's Voting in VG2 of Control Across Experiments   ///
> gen GroupAVG2ControlAcrossExps=GroupAVG2ControlAvg if Treatment==0&Experiment==1
(12,784 missing values generated)

. replace GroupAVG2ControlAcrossExps=GroupAVG2ControlAvg if Treatment==0&Experiment==2
(16 real changes made)

. ttest GroupAVG2ControlAcrossExps,by(Experiment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       1 |      16    .1203125    .0385424    .1541695    .0381614    .2024636
       2 |      16      .09375    .0350223    .1400893    .0191017    .1683983
---------+--------------------------------------------------------------------
combined |      32    .1070313    .0257262    .1455294    .0545623    .1595002
---------+--------------------------------------------------------------------
    diff |            .0265625    .0520776               -.0797942    .1329192
------------------------------------------------------------------------------
    diff = mean(1) - mean(2)                                      t =   0.5101
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.6931         Pr(|T| > |t|) = 0.6137          Pr(T > t) = 0.3069

. ranksum GroupAVG2ControlAcrossExps,by(Experiment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

  Experiment |      obs    rank sum    expected
-------------+---------------------------------
           1 |       16         278         264
           2 |       16         250         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties      -24.26
                     ----------
adjusted variance        679.74

Ho: GroupA..(Experi~t==1) = GroupA..(Experi~t==2)
             z =   0.537
    Prob > |z| =   0.5913

. ////////////////////////////////////////////////////////////////////////////////
> ///   Comparisons of Group B's Voting in VG2 of Control Across Experiments   ///
> gen GroupBVG2ControlAcrossExps=GroupBVG2ControlAvg if Treatment==0&Experiment==1
(12,784 missing values generated)

. replace GroupBVG2ControlAcrossExps=GroupBVG2ControlAvg if Treatment==0&Experiment==2
(16 real changes made)

. ttest GroupBVG2ControlAcrossExps,by(Experiment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       1 |      16    .3489583    .0519408    .2077631    .2382492    .4596675
       2 |      16    .3927083    .0453374    .1813497    .2960739    .4893428
---------+--------------------------------------------------------------------
combined |      32    .3708333    .0341385    .1931163    .3012075    .4404592
---------+--------------------------------------------------------------------
    diff |             -.04375    .0689444               -.1845532    .0970532
------------------------------------------------------------------------------
    diff = mean(1) - mean(2)                                      t =  -0.6346
Ho: diff = 0                                     degrees of freedom =       30

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.2653         Pr(|T| > |t|) = 0.5305          Pr(T > t) = 0.7347

. ranksum GroupBVG2ControlAcrossExps,by(Experiment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

  Experiment |      obs    rank sum    expected
-------------+---------------------------------
           1 |       16         259         264
           2 |       16         269         264
-------------+---------------------------------
    combined |       32         528         528

unadjusted variance      704.00
adjustment for ties       -2.71
                     ----------
adjusted variance        701.29

Ho: GroupB..(Experi~t==1) = GroupB..(Experi~t==2)
             z =  -0.189
    Prob > |z| =   0.8502

. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> 
. 
. 
. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> gen ExperimentI=0

. replace ExperimentI=1 if Experiment==1
(6,400 real changes made)

. 
. logit Voting ExperimentI if VotingGame==2&GroupA==1&Treatment==0,vce(cluster UniqueGroupIDbyElectorate)

Iteration 0:   log pseudolikelihood = -435.53674  
Iteration 1:   log pseudolikelihood = -434.35638  
Iteration 2:   log pseudolikelihood = -434.35284  
Iteration 3:   log pseudolikelihood = -434.35284  

Logistic regression                             Number of obs     =      1,280
                                                Wald chi2(1)      =       0.27
                                                Prob > chi2       =     0.6058
Log pseudolikelihood = -434.35284               Pseudo R2         =     0.0027

             (Std. Err. adjusted for 32 clusters in UniqueGroupIDbyElectorate)
------------------------------------------------------------------------------
             |               Robust
      Voting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 ExperimentI |   .2792093   .5410915     0.52   0.606    -.7813106    1.339729
       _cons |  -2.268684   .4055135    -5.59   0.000    -3.063475   -1.473892
------------------------------------------------------------------------------

. eststo margin1: margins, dydx(*) atmeans  post

Conditional marginal effects                    Number of obs     =      1,280
Model VCE    : Robust

Expression   : Pr(Voting), predict()
dy/dx w.r.t. : ExperimentI
at           : ExperimentI     =          .5 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 ExperimentI |   .0265255   .0510172     0.52   0.603    -.0734665    .1265175
------------------------------------------------------------------------------

. estimates store m1, title(Model 1)

. logit Voting ExperimentI if VotingGame==2&GroupA==0&Treatment==0,vce(cluster UniqueGroupIDbyElectorate)

Iteration 0:   log pseudolikelihood = -1266.0436  
Iteration 1:   log pseudolikelihood = -1264.0741  
Iteration 2:   log pseudolikelihood = -1264.0738  
Iteration 3:   log pseudolikelihood = -1264.0738  

Logistic regression                             Number of obs     =      1,920
                                                Wald chi2(1)      =       0.41
                                                Prob > chi2       =     0.5211
Log pseudolikelihood = -1264.0738               Pseudo R2         =     0.0016

             (Std. Err. adjusted for 32 clusters in UniqueGroupIDbyElectorate)
------------------------------------------------------------------------------
             |               Robust
      Voting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 ExperimentI |  -.1876791   .2925018    -0.64   0.521    -.7609721    .3856138
       _cons |   -.435942   .1870119    -2.33   0.020    -.8024786   -.0694054
------------------------------------------------------------------------------

. eststo margin2: margins,  dydx(*) atmeans  post

Conditional marginal effects                    Number of obs     =      1,920
Model VCE    : Robust

Expression   : Pr(Voting), predict()
dy/dx w.r.t. : ExperimentI
at           : ExperimentI     =          .5 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 ExperimentI |  -.0437757   .0679424    -0.64   0.519    -.1769403     .089389
------------------------------------------------------------------------------

. estimates store m2, title(Model 2)

. logit Voting ExperimentI if VotingGame==2&GroupA==1&Treatment==1,vce(cluster UniqueGroupIDbyElectorate)

Iteration 0:   log pseudolikelihood = -693.40045  
Iteration 1:   log pseudolikelihood = -650.94695  
Iteration 2:   log pseudolikelihood = -649.70975  
Iteration 3:   log pseudolikelihood = -649.70729  
Iteration 4:   log pseudolikelihood = -649.70729  

Logistic regression                             Number of obs     =      1,280
                                                Wald chi2(1)      =       9.30
                                                Prob > chi2       =     0.0023
Log pseudolikelihood = -649.70729               Pseudo R2         =     0.0630

             (Std. Err. adjusted for 32 clusters in UniqueGroupIDbyElectorate)
------------------------------------------------------------------------------
             |               Robust
      Voting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 ExperimentI |   1.299763   .4262513     3.05   0.002     .4643256      2.1352
       _cons |  -1.960273   .3708629    -5.29   0.000    -2.687151   -1.233395
------------------------------------------------------------------------------

. eststo margin3: margins, dydx(*) atmeans  post

Conditional marginal effects                    Number of obs     =      1,280
Model VCE    : Robust

Expression   : Pr(Voting), predict()
dy/dx w.r.t. : ExperimentI
at           : ExperimentI     =          .5 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 ExperimentI |   .2174484    .061982     3.51   0.000      .095966    .3389308
------------------------------------------------------------------------------

. estimates store m3, title(Model 3)

. logit Voting ExperimentI if VotingGame==2&GroupA==0&Treatment==1,vce(cluster UniqueGroupIDbyElectorate)

Iteration 0:   log pseudolikelihood = -1326.0219  
Iteration 1:   log pseudolikelihood = -1304.8357  
Iteration 2:   log pseudolikelihood = -1304.8321  
Iteration 3:   log pseudolikelihood = -1304.8321  

Logistic regression                             Number of obs     =      1,920
                                                Wald chi2(1)      =       4.38
                                                Prob > chi2       =     0.0364
Log pseudolikelihood = -1304.8321               Pseudo R2         =     0.0160

             (Std. Err. adjusted for 32 clusters in UniqueGroupIDbyElectorate)
------------------------------------------------------------------------------
             |               Robust
      Voting |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 ExperimentI |   .5991589   .2862913     2.09   0.036     .0380383     1.16028
       _cons |  -.4446858   .2247778    -1.98   0.048    -.8852422   -.0041295
------------------------------------------------------------------------------

. eststo margin4: margins,  dydx(*) atmeans  post

Conditional marginal effects                    Number of obs     =      1,920
Model VCE    : Robust

Expression   : Pr(Voting), predict()
dy/dx w.r.t. : ExperimentI
at           : ExperimentI     =          .5 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 ExperimentI |    .149004   .0708536     2.10   0.035     .0101336    .2878744
------------------------------------------------------------------------------

. estimates store m4, title(Model 4)

. ////////////////////////////////////////////////////////////////////////////////
> /////////        Generate Table A5 reported in Online Appendix F       /////////
> ////////////////////////////////////////////////////////////////////////////////
> esttab margin1 margin2 margin3 margin4 using TableA5.txt,cells(b(star fmt(3)) se(par fmt(3))) star(* 0.10 ** 0.05 *** 0.01) st
> ats(r2_a N,fmt(%9.3f %9.0g)) legend label collabels(none) replace
(note: file TableA5.txt not found)
(output written to TableA5.txt)

. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ///I examine whether Group A's and Group B's task performance in Treatment of Experiment I
> ///is different from Group A's and Group B's task performance in Treatment of Experiment II
> ///None of the following pairwise comparisons are statistically different at the 5% level.
> ////////////////////////////////////////////////////////////////////////////////
> ttest TaskPerformance if GroupA==1&Period==1&Treatment==1,by(Experiment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       1 |      32     16.1875    .7356661    4.161556     14.6871     17.6879
       2 |      32    16.21875    .4528903    2.561934    15.29507    17.14243
---------+--------------------------------------------------------------------
combined |      64    16.20313    .4285101    3.428081    15.34682    17.05943
---------+--------------------------------------------------------------------
    diff |             -.03125    .8638948               -1.758151    1.695651
------------------------------------------------------------------------------
    diff = mean(1) - mean(2)                                      t =  -0.0362
Ho: diff = 0                                     degrees of freedom =       62

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.4856         Pr(|T| > |t|) = 0.9713          Pr(T > t) = 0.5144

. ksmirnov TaskPerformance if GroupA==1&Period==1&Treatment==1,by(Experiment)

Two-sample Kolmogorov-Smirnov test for equality of distribution functions

 Smaller group       D       P-value  
 -----------------------------------
 1:                  0.2188    0.216
 2:                 -0.1250    0.607
 Combined K-S:       0.2188    0.428

Note: Ties exist in combined dataset;
      there are 15 unique values out of 64 observations.

. ttest TaskPerformance if GroupA==0&Period==1&Treatment==1,by(Experiment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       1 |      48    9.979167    .4530135     3.13857    9.067821    10.89051
       2 |      48    10.58333    .5496883    3.808352    9.477503    11.68916
---------+--------------------------------------------------------------------
combined |      96    10.28125    .3556262    3.484411    9.575243    10.98726
---------+--------------------------------------------------------------------
    diff |           -.6041667     .712305               -2.018465    .8101317
------------------------------------------------------------------------------
    diff = mean(1) - mean(2)                                      t =  -0.8482
Ho: diff = 0                                     degrees of freedom =       94

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.1992         Pr(|T| > |t|) = 0.3985          Pr(T > t) = 0.8008

. ksmirnov TaskPerformance if GroupA==0&Period==1&Treatment==1,by(Experiment)

Two-sample Kolmogorov-Smirnov test for equality of distribution functions

 Smaller group       D       P-value  
 -----------------------------------
 1:                  0.1458    0.360
 2:                 -0.0208    0.979
 Combined K-S:       0.1458    0.687

Note: Ties exist in combined dataset;
      there are 17 unique values out of 96 observations.

. restore

. 
. 
. 
. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ********************************************************************************
. *                                                                              *
. *                    Statistical Analysis of Experiment III                    *
. *                                                                              *
. ********************************************************************************
. preserve

. keep if Experiment==3
(12,800 observations deleted)

. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> /// In the first 15 periods of Experiment III, individuals received no feedback
> ////////////////////////////////////////////////////////////////////////////////
> //////////////    Results of Appendix G (Figure A5)     ////////////////////////
> /// I compute and compare individual level averages of voting by Subject and Treatment of Period<=15
> ////////////////////////////////////////////////////////////////////////////////
> 
. /// Group A VG1
> sort UniqueSubjectID

. by UniqueSubjectID: egen ATreatmentVG1=mean(Voting) if GroupA==1&VotingGame==1&Treatment==1&Period<=15
(3240 missing values generated)

. by UniqueSubjectID, sort: egen GroupATreatmentVG1=mean(ATreatmentVG1)
(2640 missing values generated)

. by UniqueSubjectID: gen GroupAVG1TreatmentAvg=GroupATreatmentVG1 if _n==1
(3,288 missing values generated)

. 
. sort UniqueSubjectID

. by UniqueSubjectID: egen AControlVG1=mean(Voting) if GroupA==1&VotingGame==1&Treatment==0&Period<=15
(3240 missing values generated)

. by UniqueSubjectID, sort: egen GroupAControlVG1=mean(AControlVG1)
(2640 missing values generated)

. by UniqueSubjectID: gen GroupAVG1ControlAvg=GroupAControlVG1 if _n==1
(3,288 missing values generated)

. 
. 
. gen GroupAVG1AcorssTreatments=GroupAVG1TreatmentAvg if Treatment==1
(3,288 missing values generated)

. replace GroupAVG1AcorssTreatments=GroupAVG1ControlAvg if Treatment==0
(12 real changes made)

. ttest GroupAVG1AcorssTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      12    .4333333    .0915633    .3171846    .2318039    .6348628
       1 |      12    .6666667    .0666667    .2309401    .5199343     .813399
---------+--------------------------------------------------------------------
combined |      24         .55    .0604931    .2963547    .4248604    .6751396
---------+--------------------------------------------------------------------
    diff |           -.2333333     .113262               -.4682244    .0015577
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.0601
Ho: diff = 0                                     degrees of freedom =       22

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0257         Pr(|T| > |t|) = 0.0514          Pr(T > t) = 0.9743

. ranksum GroupAVG1AcorssTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       12       113.5         150
           1 |       12       186.5         150
-------------+---------------------------------
    combined |       24         300         300

unadjusted variance      300.00
adjustment for ties      -22.96
                     ----------
adjusted variance        277.04

Ho: GroupA~s(Treatm~t==0) = GroupA~s(Treatm~t==1)
             z =  -2.193
    Prob > |z| =   0.0283

. 
. /// Group B VG1
> sort UniqueSubjectID

. by UniqueSubjectID: egen BTreatmentVG1=mean(Voting) if GroupA==0&VotingGame==1&Treatment==1&Period<=15
(3210 missing values generated)

. by UniqueSubjectID, sort: egen GroupBTreatmentVG1=mean(BTreatmentVG1)
(2310 missing values generated)

. by UniqueSubjectID: gen GroupBVG1TreatmentAvg=GroupBTreatmentVG1 if _n==1
(3,282 missing values generated)

. 
. sort UniqueSubjectID

. by UniqueSubjectID: egen BControlVG1=mean(Voting) if GroupA==0&VotingGame==1&Treatment==0&Period<=15
(3210 missing values generated)

. by UniqueSubjectID, sort: egen GroupBControlVG1=mean(BControlVG1)
(2310 missing values generated)

. by UniqueSubjectID: gen GroupBVG1ControlAvg=GroupBControlVG1 if _n==1
(3,282 missing values generated)

. 
. 
. gen GroupBVG1AcorssTreatments=GroupBVG1TreatmentAvg if Treatment==1
(3,282 missing values generated)

. replace GroupBVG1AcorssTreatments=GroupBVG1ControlAvg if Treatment==0
(18 real changes made)

. ttest GroupBVG1AcorssTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      18    .1888889    .0593477     .251791    .0636762    .3141016
       1 |      18    .4555556    .0719578     .305291    .3037379    .6073732
---------+--------------------------------------------------------------------
combined |      36    .3222222    .0511939    .3071632    .2182932    .4261513
---------+--------------------------------------------------------------------
    diff |           -.2666667    .0932742               -.4562226   -.0771107
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.8590
Ho: diff = 0                                     degrees of freedom =       34

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0036         Pr(|T| > |t|) = 0.0072          Pr(T > t) = 0.9964

. ranksum GroupBVG1AcorssTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       18         253         333
           1 |       18         413         333
-------------+---------------------------------
    combined |       36         666         666

unadjusted variance      999.00
adjustment for ties      -68.53
                     ----------
adjusted variance        930.47

Ho: GroupB~s(Treatm~t==0) = GroupB~s(Treatm~t==1)
             z =  -2.623
    Prob > |z| =   0.0087

. 
. /// Group A VG2
> sort UniqueSubjectID

. by UniqueSubjectID: egen ATreatmentVG2=mean(Voting) if GroupA==1&VotingGame==2&Treatment==1&Period<=15
(3240 missing values generated)

. by UniqueSubjectID, sort: egen GroupATreatmentVG2=mean(ATreatmentVG2)
(2640 missing values generated)

. by UniqueSubjectID: gen GroupAVG2TreatmentAvg=GroupATreatmentVG2 if _n==1
(3,288 missing values generated)

. 
. sort UniqueSubjectID

. by UniqueSubjectID: egen AControlVG2=mean(Voting) if GroupA==1&VotingGame==2&Treatment==0&Period<=15
(3240 missing values generated)

. by UniqueSubjectID, sort: egen GroupAControlVG2=mean(AControlVG2)
(2640 missing values generated)

. by UniqueSubjectID: gen GroupAVG2ControlAvg=GroupAControlVG2 if _n==1
(3,288 missing values generated)

. 
. 
. gen GroupAVG2AcorssTreatments=GroupAVG2TreatmentAvg if Treatment==1
(3,288 missing values generated)

. replace GroupAVG2AcorssTreatments=GroupAVG2ControlAvg if Treatment==0
(12 real changes made)

. ttest GroupAVG2AcorssTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      12          .1    .0522233    .1809068   -.0149427    .2149427
       1 |      12         .35    .1076611    .3729489    .1130396    .5869605
---------+--------------------------------------------------------------------
combined |      24        .225    .0640567    .3138125    .0924886    .3575114
---------+--------------------------------------------------------------------
    diff |                -.25    .1196586               -.4981568   -.0018432
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.0893
Ho: diff = 0                                     degrees of freedom =       22

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0242         Pr(|T| > |t|) = 0.0485          Pr(T > t) = 0.9758

. ranksum GroupAVG2AcorssTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       12       115.5         150
           1 |       12       184.5         150
-------------+---------------------------------
    combined |       24         300         300

unadjusted variance      300.00
adjustment for ties      -39.78
                     ----------
adjusted variance        260.22

Ho: GroupA..(Treatm~t==0) = GroupA..(Treatm~t==1)
             z =  -2.139
    Prob > |z| =   0.0325

. 
. /// Group B VG2
> sort UniqueSubjectID

. by UniqueSubjectID: egen BTreatmentVG2=mean(Voting) if GroupA==0&VotingGame==2&Treatment==1&Period<=15
(3210 missing values generated)

. by UniqueSubjectID, sort: egen GroupBTreatmentVG2=mean(BTreatmentVG2)
(2310 missing values generated)

. by UniqueSubjectID: gen GroupBVG2TreatmentAvg=GroupBTreatmentVG2 if _n==1
(3,282 missing values generated)

. 
. sort UniqueSubjectID

. by UniqueSubjectID: egen BControlVG2=mean(Voting) if GroupA==0&VotingGame==2&Treatment==0&Period<=15
(3210 missing values generated)

. by UniqueSubjectID, sort: egen GroupBControlVG2=mean(BControlVG2)
(2310 missing values generated)

. by UniqueSubjectID: gen GroupBVG2ControlAvg=GroupBControlVG2 if _n==1
(3,282 missing values generated)

. 
. 
. gen GroupBVG2AcorssTreatments=GroupBVG2TreatmentAvg if Treatment==1
(3,282 missing values generated)

. replace GroupBVG2AcorssTreatments=GroupBVG2ControlAvg if Treatment==0
(18 real changes made)

. ttest GroupBVG2AcorssTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      18    .3111111    .0779177    .3305768    .1467191    .4755031
       1 |      18    .5777778     .086906    .3687109    .3944222    .7611334
---------+--------------------------------------------------------------------
combined |      36    .4444445    .0617785    .3706708    .3190275    .5698614
---------+--------------------------------------------------------------------
    diff |           -.2666667    .1167211               -.5038725   -.0294608
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.2846
Ho: diff = 0                                     degrees of freedom =       34

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0143         Pr(|T| > |t|) = 0.0287          Pr(T > t) = 0.9857

. ranksum GroupBVG2AcorssTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       18       263.5         333
           1 |       18       402.5         333
-------------+---------------------------------
    combined |       36         666         666

unadjusted variance      999.00
adjustment for ties      -38.06
                     ----------
adjusted variance        960.94

Ho: GroupB..(Treatm~t==0) = GroupB..(Treatm~t==1)
             z =  -2.242
    Prob > |z| =   0.0250

. 
. 
. /// Group A VG3
> sort UniqueSubjectID

. by UniqueSubjectID: egen ATreatmentVG3=mean(Voting) if GroupA==1&VotingGame==3&Treatment==1&Period<=15
(3240 missing values generated)

. by UniqueSubjectID, sort: egen GroupATreatmentVG3=mean(ATreatmentVG3)
(2640 missing values generated)

. by UniqueSubjectID: gen GroupAVG3TreatmentAvg=GroupATreatmentVG3 if _n==1
(3,288 missing values generated)

. 
. sort UniqueSubjectID

. by UniqueSubjectID: egen AControlVG3=mean(Voting) if GroupA==1&VotingGame==3&Treatment==0&Period<=15
(3240 missing values generated)

. by UniqueSubjectID, sort: egen GroupAControlVG3=mean(AControlVG3)
(2640 missing values generated)

. by UniqueSubjectID: gen GroupAVG3ControlAvg=GroupAControlVG3 if _n==1
(3,288 missing values generated)

. 
. 
. gen GroupAVG3AcorssTreatments=GroupAVG3TreatmentAvg if Treatment==1
(3,288 missing values generated)

. replace GroupAVG3AcorssTreatments=GroupAVG3ControlAvg if Treatment==0
(12 real changes made)

. ttest GroupAVG3AcorssTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      12         .25    .0783349    .2713602    .0775859    .4224141
       1 |      12    .5833333    .0998737    .3459725    .3635129    .8031538
---------+--------------------------------------------------------------------
combined |      24    .4166667    .0711364    .3484957    .2695098    .5638235
---------+--------------------------------------------------------------------
    diff |           -.3333333    .1269296               -.5965691   -.0700976
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.6261
Ho: diff = 0                                     degrees of freedom =       22

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0077         Pr(|T| > |t|) = 0.0154          Pr(T > t) = 0.9923

. ranksum GroupAVG3AcorssTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       12       110.5         150
           1 |       12       189.5         150
-------------+---------------------------------
    combined |       24         300         300

unadjusted variance      300.00
adjustment for ties      -12.39
                     ----------
adjusted variance        287.61

Ho: GroupA..(Treatm~t==0) = GroupA..(Treatm~t==1)
             z =  -2.329
    Prob > |z| =   0.0199

. 
. /// Group B VG3
> sort UniqueSubjectID

. by UniqueSubjectID: egen BTreatmentVG3=mean(Voting) if GroupA==0&VotingGame==3&Treatment==1&Period<=15
(3210 missing values generated)

. by UniqueSubjectID, sort: egen GroupBTreatmentVG3=mean(BTreatmentVG3)
(2310 missing values generated)

. by UniqueSubjectID: gen GroupBVG3TreatmentAvg=GroupBTreatmentVG3 if _n==1
(3,282 missing values generated)

. 
. sort UniqueSubjectID

. by UniqueSubjectID: egen BControlVG3=mean(Voting) if GroupA==0&VotingGame==3&Treatment==0&Period<=15
(3210 missing values generated)

. by UniqueSubjectID, sort: egen GroupBControlVG3=mean(BControlVG3)
(2310 missing values generated)

. by UniqueSubjectID: gen GroupBVG3ControlAvg=GroupBControlVG3 if _n==1
(3,282 missing values generated)

. 
. 
. gen GroupBVG3AcorssTreatments=GroupBVG3TreatmentAvg if Treatment==1
(3,282 missing values generated)

. replace GroupBVG3AcorssTreatments=GroupBVG3ControlAvg if Treatment==0
(18 real changes made)

. ttest GroupBVG3AcorssTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      18    .1222222    .0432016    .1832888    .0310749    .2133696
       1 |      18    .3555556    .0922565    .3914111    .1609114    .5501997
---------+--------------------------------------------------------------------
combined |      36    .2388889    .0539367    .3236204    .1293915    .3483863
---------+--------------------------------------------------------------------
    diff |           -.2333333    .1018707               -.4403594   -.0263072
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.2905
Ho: diff = 0                                     degrees of freedom =       34

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0142         Pr(|T| > |t|) = 0.0283          Pr(T > t) = 0.9858

. ranksum GroupBVG3AcorssTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       18       275.5         333
           1 |       18       390.5         333
-------------+---------------------------------
    combined |       36         666         666

unadjusted variance      999.00
adjustment for ties     -137.57
                     ----------
adjusted variance        861.43

Ho: GroupB..(Treatm~t==0) = GroupB..(Treatm~t==1)
             z =  -1.959
    Prob > |z| =   0.0501

. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> //////////    Results of Appendix H (Figure A6 and A7)     /////////////////////
> ///To understand the influence of voting interactions on self-reported values, I asked
> ///the same survey questions in Experiment III after participants played voting games for
> ///15 periods with no feedback.
> ///compare selfreported Valuation of Participation and Earning more than others in the absence of feedback (Period<=15)
> ////////////////////////////////////////////////////////////////////////////////
> ttest VotingImportance if GroupA==1&Period==16,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      12    4.333333    .8645662    2.994945    2.430436    6.236231
       1 |      12        6.75    .5383054    1.864745    5.565198    7.934802
---------+--------------------------------------------------------------------
combined |      24    5.541667    .5581386     2.73431    4.387069    6.696264
---------+--------------------------------------------------------------------
    diff |           -2.416667    1.018453                -4.52881   -.3045234
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.3729
Ho: diff = 0                                     degrees of freedom =       22

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0134         Pr(|T| > |t|) = 0.0268          Pr(T > t) = 0.9866

. ranksum VotingImportance if GroupA==1&Period==16,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       12         115         150
           1 |       12         185         150
-------------+---------------------------------
    combined |       24         300         300

unadjusted variance      300.00
adjustment for ties      -15.00
                     ----------
adjusted variance        285.00

Ho: Votin~ce(Treatm~t==0) = Votin~ce(Treatm~t==1)
             z =  -2.073
    Prob > |z| =   0.0382

. 
. ttest VotingImportance if GroupA==0&Period==16,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      18    4.888889    .5476563    2.323509    3.733435    6.044343
       1 |      18    6.777778    .4468887    1.895988    5.834925    7.720631
---------+--------------------------------------------------------------------
combined |      36    5.833333     .383178    2.299068    5.055441    6.611226
---------+--------------------------------------------------------------------
    diff |           -1.888889      .70685               -3.325381   -.4523969
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.6723
Ho: diff = 0                                     degrees of freedom =       34

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0057         Pr(|T| > |t|) = 0.0115          Pr(T > t) = 0.9943

. ranksum VotingImportance if GroupA==0&Period==16,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       18       258.5         333
           1 |       18       407.5         333
-------------+---------------------------------
    combined |       36         666         666

unadjusted variance      999.00
adjustment for ties      -25.84
                     ----------
adjusted variance        973.16

Ho: Votin~ce(Treatm~t==0) = Votin~ce(Treatm~t==1)
             z =  -2.388
    Prob > |z| =   0.0169

. 
. ttest EarningMorethanOthers if GroupA==1&Period==16,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      12        5.75    .5657524    1.959824    4.504787    6.995213
       1 |      12    7.583333    .4680445    1.621354    6.553174    8.613492
---------+--------------------------------------------------------------------
combined |      24    6.666667    .4067664     1.99274    5.825206    7.508127
---------+--------------------------------------------------------------------
    diff |           -1.833333    .7342625               -3.356101   -.3105661
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.4968
Ho: diff = 0                                     degrees of freedom =       22

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0103         Pr(|T| > |t|) = 0.0205          Pr(T > t) = 0.9897

. ranksum EarningMorethanOthers if GroupA==1&Period==16,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       12       109.5         150
           1 |       12       190.5         150
-------------+---------------------------------
    combined |       24         300         300

unadjusted variance      300.00
adjustment for ties      -12.39
                     ----------
adjusted variance        287.61

Ho: Earnin~s(Treatm~t==0) = Earnin~s(Treatm~t==1)
             z =  -2.388
    Prob > |z| =   0.0169

. 
. ttest EarningMorethanOthers if GroupA==0&Period==16,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      18    4.666667     .588562    2.497057    3.424909    5.908424
       1 |      18    6.833333    .4142084    1.757338     5.95943    7.707237
---------+--------------------------------------------------------------------
combined |      36        5.75    .3991559    2.394935    4.939671    6.560329
---------+--------------------------------------------------------------------
    diff |           -2.166667     .719704               -3.629281   -.7040522
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -3.0105
Ho: diff = 0                                     degrees of freedom =       34

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0024         Pr(|T| > |t|) = 0.0049          Pr(T > t) = 0.9976

. ranksum EarningMorethanOthers if GroupA==0&Period==16,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       18         256         333
           1 |       18         410         333
-------------+---------------------------------
    combined |       36         666         666

unadjusted variance      999.00
adjustment for ties      -55.16
                     ----------
adjusted variance        943.84

Ho: Earnin~s(Treatm~t==0) = Earnin~s(Treatm~t==1)
             z =  -2.506
    Prob > |z| =   0.0122

. restore

. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> //////////                 Results of Appendix I           /////////////////////
> preserve

. keep if Experiment==3
(12,800 observations deleted)

. keep if Period>15
(900 observations deleted)

. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> /// I compute and compare individual level averages of voting by Subject and Treatment of Period>15
> ////////////////////////////////////////////////////////////////////////////////
> 
. /// Group A VG1
> sort UniqueSubjectID

. by UniqueSubjectID: egen ATreatmentVG1=mean(Voting) if GroupA==1&VotingGame==1&Treatment==1
(2160 missing values generated)

. by UniqueSubjectID, sort: egen GroupATreatmentVG1=mean(ATreatmentVG1)
(1920 missing values generated)

. by UniqueSubjectID: gen GroupAVG1TreatmentAvg=GroupATreatmentVG1 if _n==1
(2,388 missing values generated)

. 
. sort UniqueSubjectID

. by UniqueSubjectID: egen AControlVG1=mean(Voting) if GroupA==1&VotingGame==1&Treatment==0
(2160 missing values generated)

. by UniqueSubjectID, sort: egen GroupAControlVG1=mean(AControlVG1)
(1920 missing values generated)

. by UniqueSubjectID: gen GroupAVG1ControlAvg=GroupAControlVG1 if _n==1
(2,388 missing values generated)

. 
. 
. gen GroupAVG1AcorssTreatments=GroupAVG1TreatmentAvg if Treatment==1
(2,388 missing values generated)

. replace GroupAVG1AcorssTreatments=GroupAVG1ControlAvg if Treatment==0
(12 real changes made)

. ttest GroupAVG1AcorssTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      12          .4    .0753778    .2611165    .2340945    .5659055
       1 |      12       .6625    .0868482    .3008511    .4713484    .8536517
---------+--------------------------------------------------------------------
combined |      24      .53125    .0625407    .3063858    .4018746    .6606254
---------+--------------------------------------------------------------------
    diff |              -.2625    .1149975               -.5009903   -.0240097
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.2827
Ho: diff = 0                                     degrees of freedom =       22

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0162         Pr(|T| > |t|) = 0.0325          Pr(T > t) = 0.9838

. ranksum GroupAVG1AcorssTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       12         112         150
           1 |       12         188         150
-------------+---------------------------------
    combined |       24         300         300

unadjusted variance      300.00
adjustment for ties       -3.26
                     ----------
adjusted variance        296.74

Ho: GroupA~s(Treatm~t==0) = GroupA~s(Treatm~t==1)
             z =  -2.206
    Prob > |z| =   0.0274

. 
. /// Group B VG1
> sort UniqueSubjectID

. by UniqueSubjectID: egen BTreatmentVG1=mean(Voting) if GroupA==0&VotingGame==1&Treatment==1
(2040 missing values generated)

. by UniqueSubjectID, sort: egen GroupBTreatmentVG1=mean(BTreatmentVG1)
(1680 missing values generated)

. by UniqueSubjectID: gen GroupBVG1TreatmentAvg=GroupBTreatmentVG1 if _n==1
(2,382 missing values generated)

. 
. sort UniqueSubjectID

. by UniqueSubjectID: egen BControlVG1=mean(Voting) if GroupA==0&VotingGame==1&Treatment==0
(2040 missing values generated)

. by UniqueSubjectID, sort: egen GroupBControlVG1=mean(BControlVG1)
(1680 missing values generated)

. by UniqueSubjectID: gen GroupBVG1ControlAvg=GroupBControlVG1 if _n==1
(2,382 missing values generated)

. 
. 
. gen GroupBVG1AcorssTreatments=GroupBVG1TreatmentAvg if Treatment==1
(2,382 missing values generated)

. replace GroupBVG1AcorssTreatments=GroupBVG1ControlAvg if Treatment==0
(18 real changes made)

. ttest GroupBVG1AcorssTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      18    .2388889    .0590717    .2506201    .1142584    .3635194
       1 |      18    .4916667    .0716575    .3040172    .3404825    .6428509
---------+--------------------------------------------------------------------
combined |      36    .3652778    .0505061    .3030369    .2627448    .4678107
---------+--------------------------------------------------------------------
    diff |           -.2527778     .092867               -.4415062   -.0640494
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.7219
Ho: diff = 0                                     degrees of freedom =       34

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0051         Pr(|T| > |t|) = 0.0102          Pr(T > t) = 0.9949

. ranksum GroupBVG1AcorssTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       18       255.5         333
           1 |       18       410.5         333
-------------+---------------------------------
    combined |       36         666         666

unadjusted variance      999.00
adjustment for ties      -11.06
                     ----------
adjusted variance        987.94

Ho: GroupB~s(Treatm~t==0) = GroupB~s(Treatm~t==1)
             z =  -2.466
    Prob > |z| =   0.0137

. 
. /// Group A VG2
> sort UniqueSubjectID

. by UniqueSubjectID: egen ATreatmentVG2=mean(Voting) if GroupA==1&VotingGame==2&Treatment==1
(2160 missing values generated)

. by UniqueSubjectID, sort: egen GroupATreatmentVG2=mean(ATreatmentVG2)
(1920 missing values generated)

. by UniqueSubjectID: gen GroupAVG2TreatmentAvg=GroupATreatmentVG2 if _n==1
(2,388 missing values generated)

. 
. sort UniqueSubjectID

. by UniqueSubjectID: egen AControlVG2=mean(Voting) if GroupA==1&VotingGame==2&Treatment==0
(2160 missing values generated)

. by UniqueSubjectID, sort: egen GroupAControlVG2=mean(AControlVG2)
(1920 missing values generated)

. by UniqueSubjectID: gen GroupAVG2ControlAvg=GroupAControlVG2 if _n==1
(2,388 missing values generated)

. 
. 
. gen GroupAVG2AcorssTreatments=GroupAVG2TreatmentAvg if Treatment==1
(2,388 missing values generated)

. replace GroupAVG2AcorssTreatments=GroupAVG2ControlAvg if Treatment==0
(12 real changes made)

. ttest GroupAVG2AcorssTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      12    .0916667    .0373524    .1293925    .0094546    .1738788
       1 |      12    .3791667    .1057904    .3664686    .1463236    .6120097
---------+--------------------------------------------------------------------
combined |      24    .2354167    .0625166    .3062676    .1060912    .3647421
---------+--------------------------------------------------------------------
    diff |              -.2875    .1121909               -.5201698   -.0548302
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -2.5626
Ho: diff = 0                                     degrees of freedom =       22

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0089         Pr(|T| > |t|) = 0.0178          Pr(T > t) = 0.9911

. ranksum GroupAVG2AcorssTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       12         109         150
           1 |       12         191         150
-------------+---------------------------------
    combined |       24         300         300

unadjusted variance      300.00
adjustment for ties      -10.04
                     ----------
adjusted variance        289.96

Ho: GroupA..(Treatm~t==0) = GroupA..(Treatm~t==1)
             z =  -2.408
    Prob > |z| =   0.0160

. 
. /// Group B VG2
> sort UniqueSubjectID

. by UniqueSubjectID: egen BTreatmentVG2=mean(Voting) if GroupA==0&VotingGame==2&Treatment==1
(2040 missing values generated)

. by UniqueSubjectID, sort: egen GroupBTreatmentVG2=mean(BTreatmentVG2)
(1680 missing values generated)

. by UniqueSubjectID: gen GroupBVG2TreatmentAvg=GroupBTreatmentVG2 if _n==1
(2,382 missing values generated)

. 
. sort UniqueSubjectID

. by UniqueSubjectID: egen BControlVG2=mean(Voting) if GroupA==0&VotingGame==2&Treatment==0
(2040 missing values generated)

. by UniqueSubjectID, sort: egen GroupBControlVG2=mean(BControlVG2)
(1680 missing values generated)

. by UniqueSubjectID: gen GroupBVG2ControlAvg=GroupBControlVG2 if _n==1
(2,382 missing values generated)

. 
. 
. gen GroupBVG2AcorssTreatments=GroupBVG2TreatmentAvg if Treatment==1
(2,382 missing values generated)

. replace GroupBVG2AcorssTreatments=GroupBVG2ControlAvg if Treatment==0
(18 real changes made)

. ttest GroupBVG2AcorssTreatments,by(Treatment)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |      18    .3222222    .0737889      .31306    .1665412    .4779033
       1 |      18    .6277778     .068148    .2891276     .483998    .7715575
---------+--------------------------------------------------------------------
combined |      36        .475    .0558307     .334984    .3616577    .5883423
---------+--------------------------------------------------------------------
    diff |           -.3055556    .1004438                -.509682   -.1014291
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -3.0421
Ho: diff = 0                                     degrees of freedom =       34

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0023         Pr(|T| > |t|) = 0.0045          Pr(T > t) = 0.9977

. ranksum GroupBVG2AcorssTreatments,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
           0 |       18         245         333
           1 |       18         421         333
-------------+---------------------------------
    combined |       36         666         666

unadjusted variance      999.00
adjustment for ties       -5.14
                     ----------
adjusted variance        993.86

Ho: GroupB..(Treatm~t==0) = GroupB..(Treatm~t==1)
             z =  -2.791
    Prob > |z| =   0.0052

. 
. restore

. ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> ////////////////////////////////////////////////////////////////////////////////
> //////////////            Results of Appendix J         ////////////////////////
> ///The results are based on the data of Current Population Survey, Voting and Registration Supplements 1968 to Present, histor
> ical table A-1. 
> ///Publicly available: https://www.census.gov/data/tables/time-series/demo/voting-and-registration/voting-historical-time-seri
> es.html.
> 
. log close OuPowerPaper
      name:  OuPowerPaper
       log:  D:\JoPReplication.log
  log type:  text
 closed on:  12 Dec 2022, 14:53:01
--------------------------------------------------------------------------------------------------------------------------------
